• Derivative Valuation-How to Price a Convertible Bond
  • Morgan Stanley just issued an ominous forecast for the rest of 2018 — and it should have traders worried that markets are peaking
    Morgan Stanley says the easy conditions enjoyed by stock traders over the past several years are rapidly coming to an end. The firm provides a specific forecast for when various asset classes will see their cyclical peaks — and spoiler alert, it's coming soon. The past couple years have been exceedingly easy for investors. It may not seem that way to traders who have battled on the front lines through rough patches and geopolitical scares, but Morgan Stanley says that once people have the benefit of hindsight, they'll realize just how perfect conditions were. Let's take an inventory of all the positive forces that support this view: stronger-than-expected economic growth, surprisingly weak inflation, continued monetary accommodation, and positive policy action (in this case, the new tax law). As Andrew Sheets, Morgan Stanley's chief cross-asset strategist, puts it, "one doesn't usually get all of those things together, and their confluence powered risk assets higher." But, unfortunately for investors, the firm also says those easy gains are all but over. Stocks have historically topped nine to 12 months after a trough in credit spreads, according to Morgan Stanley, which says such a bottom was reached in late January or early February. That, in turn, would mean equities are on pace to top around December of this year. The firm also notes 10-year Treasury yields tend to peak roughly three months before stocks, putting their top in September. Morgan Stanley has responded to its findings by reducing its net long equity exposure to 2%, down from 4%. After all, although he acknowledges it's "risky" to own stocks as they enter the final phase of a market cycle, Sheets doesn't want to miss out on the intermediate-term gains he expects them to generate. While other pundits across Wall Street haven't issued such a specific timeframe for an equity market top, firms including Goldman Sachs and BlackRock have started highlighting what they see as slowing stock fundamentals. Of particular concern is plateauing earnings growth. Richard Turnill, global chief investment strategist at BlackRock, said on Monday that "earnings are close to a peak," noting that the new tax law provided a one-time surge in profit estimates that will be impossible to surmount in the near future. Goldman has similar thoughts. As pointed out by David Kostin, the firm's chief US equity strategist, "analysts do not expect the conditions that led to upside in 1Q EPS to persist for the remainder of the year." None of this is intended to scare anyone at present time — nor should it stir up immediate worry. The bigger takeaway is that stock investors who have enjoyed such an easy run will now have to work a little harder to make money. Only time will tell if they're up for the challenge. SEE ALSO: 'Comfort is not your friend' — The stock market's biggest bear explains why the next market crash will be one of the worst ever Join the conversation about this story » NOW WATCH: I ate nothing but 'healthy' fast food for a week — here’s what happened Read more Derivative Valuation
  • 'America First' should start with the plight of the country's abandoned Native population
    Native-Americans suffer from what is known as the Asterix problem: Their numbers are too small to have a major macroeconomic impact, and thus their plight as a minority is often ignored. "This section of our population has been invisible — [seen as] too small or insignificant,” Patrice Kunesh,  director of the Minneapolis Fed's Center for Indian Country Development, told Business Insider.  During 2011-2015, the share of American Indian men ages 16-64 who were without jobs was 49%, compared with 19% for non-Hispanic white men. For women it was 47% compared with 23%. Most Americans have no idea what the term "Asterix Nation" means — but the idea is all too familiar to nearly 7 million Native Americans. President Donald Trump often touts his agenda as putting “America First,” a disturbing choice of words since the expression can be traced back to the American Nazi and white supremacist movements of the 1920s. But what that language clearly neglects, apart from America’s history as a nation of immigrants and descendants of slaves, is that the first people to live on this continent’s soil did not come from Europe at all. "It’s called the Asterix problem — this section of our population has been invisible — [seen as] too small or insignificant," said Patrice Kunesh, assistant vice president at the Federal Reserve Bank of Minneapolis, and director of the regional central bank’s Center for Indian Country Development. "We’re trying to make it visible and make it matter because of as over 1.5% of the population we have 70 million acres of land," Kunesh, who is of Standing Rock Lakota descent, told Business Insider. "They used to call it the Indian problem, they sort of foisted it on the Indian people. It’s not the Indian problem. There are many ways to advance and resolve these issues but we have to be part of the conversation first." It’s certainly an uphill battle. Just try doing a quick internet search for basic economic statistics relating to Native Americans — the data is scant and often outdated. Here’s what we do know, thanks to the Minneapolis Fed’s own research — many of the numbers are truly unsettling:  During 2011-2015, the share of American Indian men ages 16-64 who were without jobs was 49%, compared with 19% for non-Hispanic white men. Meanwhile, the share of Native American women without jobs was 47% compared with 23% for non-Hispanic white women. Many of the more than 5,000 Native children under the age of five in Minnesota are at risk of starting school behind, dropping out of school and adopting unhealthy lifestyles. The teen pregnancy rate for Native Americans ages 15-19 in Minnesota is the highest compared with other races (41.3 per 1,000). In 2015, the rate was four times higher than non-Hispanic Whites. The infant mortality rate for Native Americans (9.1 per 1,000 births in 2008-2012) is more than twice the rate for Whites (4.3 per 1,000 births). In 2012-2014, almost 40% of Native American mothers reported they smoked during the last three months of pregnancy compared with 12% of non-Hispanic Whites. In 2012-2014, 33% of Native American pregnant women experienced food insecurity 12 months before their baby was born. Food insecurity is defined as getting emergency food from a church, a food pantry, or a food bank, or eating in a food kitchen. In 2015, 7.2% of Native American births were considered low birthweight (under 5 lbs, 8 oz), increasing vulnerability to complications during infancy and later health problems. This trend is increasing – numbers are up from 5.1% in 2007. In comparison, 4.1% of non-Hispanic White births were low birthweight in 2015. Many Native American children are vulnerable to food insecurity. 60% of Native American children under the age of 6 were enrolled in the Supplemental Nutrition Assistance Program (SNAP) in 2016. According to a Bloomberg analysis of Labor Department data, about two-thirds of the 27 US counties with a majority American Indian or Alaska Native population had unemployment rates last year above the national level, with nine at 10% or higher. That contrasts with a national unemployment rate that fell to 3.9% last month, the first reading below 4% since late 2000. Many of the counties are in the Dakotas and Alaska, the Bloomberg report said. Unemployment rates varied, ranging from 3.5% to a stunning 21%. The overall jobless rate for American Indians and Alaska Natives was 8.9% in 2016, compared with 4.9% for the country as a whole. Filling a void For Kunesh, bringing attention to such disparities was the first order of business when she accepted the position to lead the Minneapolis Fed’s Center for Indian Country Development. "We started the center in 2015. I was working Washington as undersecretary for rural development in the Agriculture Department," she said. "I really did not know what that entailed but it sounded very exciting, very thrilling, to have the resources and the focus of the Fed" on Native American issues. She quickly realized the Fed was just “the kind of brain-powerhouse that Indian Country needs. We have been invisible and most of the visibility is around these really atrocious mascots and other really negative things. "I wanted to show the real story, the lived story, and I wanted to make Indian Country visible. We have to look at this from a historical trauma perspective," she said. Because of the tragic history of Native-American genocide and the confinement of the remaining population into reservations around the country, land issues are particularly important for Indian Country development. That’s because all reservation land is federal land, which means borrowers have a harder time convincing lenders that they possess adequate collateral for loans. "We started our work in the area of homeownership three years ago — because at rural development I saw the real power, the real influence that having a safe, secure house and home can provide a family and a community," Kanesh said. "And in Indian Country we know that there’s such a dire need for housing. There’s terrible over-crowdedness, the quality of the homes is really very poor." Businesses face similar obstacles and prejudices.  Kanesh says one role the Fed can play is to be a facilitator of connections between financial institutions and would-be borrowers in Indian Country, helping to overcome some of the misconceptions that she says tend to accompany the notion of doing business on reservation land. “We’re trying to bring to life the real story that’s happening in Indian country, framed in the world of economic analysis, but also tie it to the economic drivers or detractors affecting it,” she said. SEE ALSO: A single speech from a top Fed official shows why the imperative of racial and economic diversity is so much more than just lip-service Join the conversation about this story » NOW WATCH: Ian Bremmer: Why the American dream doesn't exist anymore Read more Derivative Valuation
  • A 'self-fulfilling prophecy' is making the housing market more hellish for first-time buyers
    The share of Americans who think now is a good time to buy because home prices won't fall is at a record high, according to the University of Michigan's consumer sentiment survey. This is creating a self-fulfilling prophecy that's making housing more unaffordable for first-time buyers, according to David Rosenberg, Gluskin Sheff's chief economist.  Home prices are near record highs in many cities across America, and the belief they'll continue rising is encouraging more people to buy.  The result is a higher barrier to entry for people who want to buy their first homes, according to David Rosenberg, the chief economist at Gluskin Sheff.  He drew his most recent observations on the housing market from the University of Michigan's monthly survey that checks the consumer's pulse on various parts of the economy.  The interesting housing tidbits in the latest survey, released on Friday, showed:  The share of people who cite rising prices as the reason why it's a good time to buy is at the highest level of the survey's history, going back to the late 1980s. It's "a case of expected asset inflation becoming a self-fulfilling prophecy," Rosenberg said in a note on Tuesday. What that means is, if more people want houses because prices are rising, prices will rise even more.  A record 59% of people believe that home prices will rise in the coming year, as the chart shows.  The share of people who see it as a good time to buy because of low prices is near a record low in April. "So nobody is purchasing a home because they are cheap...principally because there are no cheap homes anywhere (at least in any desirable areas)," Rosenberg said.  Lastly, the index that tracks people who say buying a home today is a bad idea because of high prices was at a five-month high in April. "This speaks to stretched affordability for first-time buyers," he said.  First-time buyers, with zero equity stored in another home, are confronted with the toughest hurdle even though they're in the minority of buyers. According to the National Association of Realtors, first-time buyers were involved in 30% of home sales in March, down from 32% a year ago.  Rosenberg questioned whether all this shows that the next housing bubble is forming — an important one to ponder a decade after the financial crisis. Unlike the previous run up in prices, however, this rise is not underpinned by low-credit borrowers and investment products that bundled risky mortgages together.   SEE ALSO: 'A difficult pill to swallow:' California's housing industry is bracing for a new regulation that could make its affordability crisis worse Join the conversation about this story » NOW WATCH: Why it's so hard for millennials to buy homes Read more Derivative Valuation
  • US IPO Weekly Recap: Pluralsight Pops 39%, With More Unicorns On The Way
    And 65% now trade above issue, up from 57%. For the second consecutive week, the VIX Volatility Index stayed below 15, a good sign for upcoming ...Read more Derivative Valuation
  • Black Swan and Volatility of Volatility
    We have written many blog posts about the increase in volatility of volatility. See, for example Is Volatility of Volatility Increasing? What Caused the Increase in Volatility of Volatility? Similarly, last week Bloomberg reported, The sudden rise in volatility in February and March showed that even with strong growth fundamentals, financial markets remain vulnerable. Since 2008, there have been seven flash crashes followed by sudden recoveries. Volatility has become binary, with markets swinging between periods of shock and calm. The VIX index traded at a median of 16 after the start of QE and at 18 before, but the spikes in volatility have become twice as frequent. It is the equivalent of swapping a stable drizzle rain with many days of scorching sun, at the price of occasional natural disasters. Read more [caption id="attachment_454" align="aligncenter" width="628"] VVIX (volatility of volatility index) as at March 23 2018. Source:[/caption] The rise of the volatility of volatility increases the chance of a Black Swan event happening. Recently, we presented a study showing that a down day of 4% during a bull market is a very rare event. It happened on February 5, and before that the last time this occurred, it was 18 years ago. We next counted the number of days when the SP500 dropped 4% or more during a bull market. We defined the bull market as price > 200-Day simple moving average.  Since 1970 there have been 5 occurrences, i.e. on average once every 10 years. We don’t know whether this qualifies as a black swan event, but a drop of more than 4% during a bull market is indeed very rare. Read more Similarly, AQR looked at the February 5 event from the implied/realized volatility perspective. ... As of now (no predictions going forward!) this recent wild period is not super crazy when we look just at volatility itself (it’s high, but not super high vs. history). But, when we look at it as a surprise (by comparing the realized 5-day volatility to the starting VIX) it’s a considerably more shocking event, though still not unprecedented. Similar events have occurred five or so times in the 1990 - present history (again, see the above figure). Finally, when just using the simple method of targeting constant volatility that we employ here, this recent surprise swoon was, as we’d expect, pretty bad for volatility targeters. But, over the longer term, volatility targeting, even the super simple volatility targeting our toy risk-model employs, may, on average, deliver more downside stability than not volatility targeting and implicitly letting the market dictate the volatility of your investment. Read more Again, from the implied/realized volatility point of view, the recent event was a rare occurrence, though not unprecedented. In times like this, risk management is more important than ever. Article Source Here: Black Swan and Volatility of Volatility Read more Derivative Valuation
  • May 18 <b>VIX</b> Trader Webinar: <b>Volatility</b> Muted Amid Rising Bond Yields
    The CBOE VIX (NYSEARCA:VXX) finished moderately higher this week, although gains in equity markets also slowed amid rising bond yields.Read more Derivative Valuation
  • How banks rank on offering the features consumers say are critical for choosing a bank
    This is a preview of a research report from Business Insider Intelligence, Business Insider's premium research service. This report is exclusively available to enterprise subscribers. Check to see if your company has access.  Banks are going to new lengths to attract and retain customers with mobile features.  In Business Insider Intelligence's Mobile Banking Competitive Edge study, 83% of respondents said they use mobile banking. And banks are investing in mobile banking capabilities at unprecedented levels: Bank of America tripled its 2015 mobile banking budget in 2016, and maintained it through 2017, for example. Cutting-edge banking services are “table-stakes to attract and retain customers,” according to Michelle Moore, Head of Digital at Bank of America. Business Insider Intelligence’s first Mobile Banking Competitive Edge Report identifies which mobile banking and emerging features are most important to consumers when choosing a bank. The study ranks the largest 15 banks and credit unions in the US by whether they offer the mobile features that customers say they care most about. The report helps channel strategists choose which features they should focus their attention on, and lets them see how they compare to rival banks in offering those features.  This study uses exclusive data from the BI Insiders Panel (BIIP), an exclusive online community of 17,000 of our readers from all over the world. Designed to be a leading-edge indicator of what’s next in digital, BIIP members tend to be affluent, tech-savvy early adopters. This means that the BIIP community is an especially sensitive indicator of what consumers will buy and adopt, as well as what behaviors, devices, and platforms will be the winners in digital disruption.  Here are some of the key takeaways from the report: Wells Fargo leads the pack. The bank offers in-demand mobile transfer capabilities, along with competitive features related to security and mobile wallets. USAA follows closely behind in second. Bank of America and Citi are tied for third, and Capital One rounds out the top five. Mobile transfers are the most in-demand mobile features. Transfers are the most important category of features to consumers when choosing a bank, according to our study. The most in-demand feature in this study, instant transfers, is in this category. Transfers also include bill pay, international transfers, and peer-to-peer (P2P) payments. Post-Equifax, consumer interest in security tools is high. Security and control was the second most popular category in the study. Gen Xers value several features in this category — such as setting travel notifications and mobile access to ATMs — more than millennials. Interest in advanced mobile banking account access is poised to jump. The account access section, the third most popular in this study, includes features like biometrics and account aggregation. With Face ID giving customers a new way to log in to banking, interest in the group of features will likely rise. In spite of lagging adoption, interest in mobile wallets is still healthy. This category weighs not only whether banks support provisioning their cards in each of the popular wallets, but if they offer their own bank-branded wallets. Our study shows consumers rank support of third-party wallets as much more important than banking solutions. Conversational features have the lowest demand in the study. The voice- or chatbot-based banking tools in the category are desired by only a small fraction of consumers. Instead of using the features to attract new customers, banks are exploring offloading costly transitional conversations with live support staff to AI.   In full, the report: Shows how 32 mobile features stack up according to how important consumers say they are for choosing a new bank. Ranks the top 15 banks on whether they offer each of those features. Analyzes how demographics effect demand for different mobile features. Provides strategies for banks to best attract and retain customers with mobile features. The full report is available to Business Insider Intelligence enterprise clients. To learn more about this report, email Senior Account Executive Chris Roth ( Business Insider Intelligence's Mobile Banking Competitive Edge study includes: Bank of America, BB&T, Capital One, Chase, Citibank, Fifth Third, HSBC, Key Bank, Navy Federal Credit Union, PNC, SunTrust, TD, US Bank, and USAA. Join the conversation about this story » Read more Derivative Valuation
  • The most expensive city in the world may build 100-square foot 'tube homes' to alleviate its escalating housing crisis
    Hong Kong has one of the worst housing crises in the world, and has been ranked the least affordable city for housing for the last eight years. Hong Kong architect James Law has designed a low-cost solution to the problem: stackable, retro-fitted water pipe "tube homes" called "O-Pods" that could be rented cheaply to young people. Law sees the design as an "open-source" solution for housing crises around the world. The first O-Pod development is being built in Shenzhen, China and due to open in July. Hong Kong has one of the worst housing crises in the world, with property prices so high that a single parking spot sold for $664,000 last year and all but the wealthiest are stuck renting tiny apartments with an ever-proliferating range of colorful names: micro-flats, nano apartments, coffin apartments, and cage homes. It's gotten so bad that the city has been ranked the least affordable city for housing in the world for eight years running, according to the Annual Demographia International Housing Affordability Survey. "We are facing a tangible affordability problem in our cities," architect James Law told Business Insider. "It is almost beyond the reach of most people to afford to live in a proper home in Hong Kong Law thinks he may have a solution: a retro-fitted concrete water pipe.  The idea came to him last August when he was overseeing a construction site. He noticed some leftover concrete pipes at the site and found that they were large, strong, safe, and not being used. Law designed and built the prototype for the O-Pod in less than a month. The O-Pod wasn't Law's first "crazy project" — he tries to challenge himself with one each year — but it is the first to garner attention across the world. Within months, the O-Pod had been written up in the New Y0rk Times, the South China Morning Post, BBC News, and Business Insider. And he has received inquiries about the design from firms in New Zealand, South Africa and Hawaii. In April, Law signed a contract with a developer in Shenzhen, China to build the first O-Pod complex. "​The big dream of mine is not necessarily me doing it, but a global community of people who share the same values using this as an open source design to share around the world," Law said.  "If we can work with governments, and even private landowners and manufacturers, we could very cheaply build the O-Pods, and we could rent them out very cheaply to young people who are struggling to afford housing." Law recently gave us a tour of the prototype and revealed where he wants to take it from here. Here's what it was like: SEE ALSO: I rode China's superfast bullet train that could go from New York to Chicago in 4.5 hours — and it shows how far behind the US really is DON'T MISS: I visited the viral, 1,400-foot glass bridge in China — and it was a traveler's worst nightmare The prototype of the O-Pod is located beneath a bridge in Kwun Tong, a former manufacturing area in East Kowloon. The O-Pod is made from two sections of concrete drain pipe and has a living space of around 100 square feet. Law's goal for the O-Pod was to create something that was cheap, easily maintained, and quickly built. Key to keeping the costs down is using a pre-manufactured product, according to Law. "When you build it yourself, it's expensive and requires labor, quality control, and testing," Law said. But because the O-Pod uses concrete water pipes, which are already being mass-manufactured, they are "low-cost, well-engineered,  and being concrete, these pipes have good insulation properties."       Designed to go underground, they are also extremely strong and can be stacked on top of each other to immediately become a building, without having to build additional ‘bookcase’ structures, columns and beams, etc [as is the case with shipping containers].” The O-Pod feels bright and spacious when you step inside. Though the floor space is 100 square feet, the curved walls and the tilted lights make it feel much bigger. See the rest of the story at Business Insider Read more Derivative Valuation
  • GOLDMAN SACHS: Oil is one of the hottest investments right now — but a dangerous mantra is robbing them of huge returns
    Commodities are the best-performing asset class year to date. Even with oil recovering by more than 50% over the past year, some investors are still skittish about the asset class. "These are dangerous words from a risk-management perspective," Goldman Sachs' commodity strategists said about the justification they keep hearing. Commodities are this year's best-performing asset class, with crude oil continuing to recover from its worst crash in over four decades. But the lingering impact of that crash is precisely why many investors are still nervous about diving in, to the dissatisfaction of Goldman Sachs' commodity strategists. They've been overweight the asset class since 2016, and they said in March that there was no better time in the past decade to invest in commodities. "Surprisingly, markets remain complacent," Jeff Currie, the firm's global head of commodities, said in a note on Wednesday. "Oil speculative net long positions have been declining since $73/bbl with the common manta, [sic] 'we will ride this one out.' These are dangerous words from a risk management perspective." Brent crude oil, the international benchmark, traded up 0.91% to $80 a barrel on Thursday, or nearly 10% above the level at which traders started paring bets that oil would rise. Brent has gained nearly 52% over the past year as some OPEC producers including Saudi Arabia implemented production limits more aggressively than expected. More recently, supply concerns mounted over Iranian oil as the US announced it was exiting the nuclear deal. Currie and his team see Brent rising to as high as $82.50 a barrel. They raised their forecast for the S&P GSCI commodity index returns this year to 8% from 5%. "This current rally has room to run, particularly from a returns perspective, as the current fundamental backdrop for oil is now more bullish than we had expected as strong demand now faces supply disappointments," Currie said. He's referring to the fact that first-quarter production levels for various producers outside the US, and globally, fell short of forecasts made by the International Energy Agency. The length of this economic expansion — now the second-longest ever — is another reason investors are skittish. That's because, as Currie illustrated in a previous note, returns are usually very weak during the early contraction and recovery phases of the cycle. They are usually marked by production that exceeds demand, just as we witnessed a few years ago with the boom of US shale oil and Saudi Arabia's response. Currie added that oil supply from OPEC usually doesn't catch up to demand this late in the economic cycle to refill inventories before a recession hits. "Growth concerns will likely prove temporary, realized demand remains robust and OPEC has never been able to catch late-cycle demand growth to replenish inventories before a recession occurs," Currie said. "And even if growth were to decelerate sharply, it would take global GDP growth collapsing to 2.5% yoy to simply balance the oil market! As a result, we highly recommend not 'riding this one out.'" SEE ALSO: Bank of America says oil could surge back to $100, and lays out exactly how it could get there Join the conversation about this story » NOW WATCH: Jeff Bezos reveals what it's like to build an empire and become the richest man in the world — and why he's willing to spend $1 billion a year to fund the most important mission of his life Read more Derivative Valuation
  • Reversal Time? <b>VIX</b> Mid-Term Futures Proshares (VIXM) Schaff Indicator Nearing Key Levels
    VIX Mid-Term Futures Proshares (VIXM) are in trader's focus this week as the ... The volatility of today's markets can test the nerves of any investor.Read more Derivative Valuation
  • Overnight Index Swap Discounting
    The overnight index swap (OIS) has come into the spotlight recently, due to the widening of the Libor-OIS spread. For example, the Economist recently reported: WATCHING financial markets can be like watching a horror film. A character walks into the darkness alone. A floorboard creaks. The latest spooky sign is the spread between the three-month dollar London interbank offered rate (LIBOR) and the overnight index swap (OIS) rate. It usually hovers at around 0.1%, but has recently climbed to 0.6% (see chart). As it widens, bankers are bracing for a jump scare. To see why, consider what each rate represents. LIBOR is the rate that banks charge other banks for unsecured loans. The OIS rate measures expectations for the federal funds rate, which is set by the central bank. As LIBOR rises above the OIS rate, that suggests banks fear it is getting riskier to lend to each other. (The gap was 3.65 percentage points in the depths of the crisis, after Lehman Brothers filed for bankruptcy.) Read more [caption id="attachment_459" align="aligncenter" width="628"] Libor-OIS spread as at May 2, 2018. Source: Bloomberg[/caption] What exactly is an overnight index swap? An overnight index swap is a fixed/floating interest rate swap that involves the exchange of the overnight rate compounded over a specified term and a fixed rate. The floating leg of the swap is related to an index of an overnight reference rate, for example Canadian Overnight Repo Rate Average (CORRA) in Canada or Fed Funds rate in the US. Usually, for swaps with maturities of 1 year or less there is only one payment. Beyond the tenor of 1 year, there are multiple payments at regular intervals. At the inception of the swap, the par swap rate makes the value of swap zero. That is, the net present value (NPV) of the fixed leg equals the NPV of the floating leg, where N denotes the notional amount of the swap, Ri-1,i is the forward OIS rate, Zi is the discount factor at time ti is the daily accrual factor, and  sK is the par swap rate of a swap with maturity tK. The OIS discount factors (DF) are often used to value interest rate derivatives that require a posting of collateral.  The OIS discount factor curve is built by bootstrapping from the short maturity and long maturity overnight index swap rates in order of increasing maturity.  The processes for backing out the discount factors from the short and long maturity swap rates are, however, different. In the short end of the curve, given that there is only 1 payment, the discount factor is calculated based on the spot rates. At the long end of the curve, the DF curve is determined as follows, Payment dates are generated at each 6 months (or a year, depending on the currency) from the time zero up to 30 years, Par swap rates are determined at each payment date. To obtain the par swap rates for the payment dates where there are no swap quotes, one linearly interpolates the par swap rates in order to complete the long end of the swap curve, Using the par swap rates at each payment date, discount factors are obtained by solving a recursive equation. This is just an introduction to OIS discounting. The process for building an OIS discount curve involves many technical details. We are happy to answer your questions. Post Source Here: Overnight Index Swap Discounting Read more Derivative Valuation