Derivative Valuation, Risk Management, Volatility Trading
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We have written about how the increase in popularity of VIX-related Exchange Traded Products could impact the financial market:
Is Volatility of Volatility Increasing? What Caused the Increase in Volatility of Volatility? Recently, Goldman Sachs derivatives analyst Rocky Fishman expressed concerns regarding the impact of VIX ETPs positions on the markets. Fishman wrote to clients early Thursday morning that he has no concerns about the net number of shorts but is concerned about the impact a sudden rise in the VIX futures would have on derivative products. He notes that over the past few weeks net positioning in VIX ETPs has gone short for only the second time in their eight year history. The analyst believes “the potential for short and levered ETPs to start buying VIX futures quickly on a sudden vol spike has grown” which in turn makes short-date VIX-based hedges timely. Therefore, his biggest concern is a one-day, end-of-day vol spike should the SPX selloff near the end of the trading day which would push issuers to replace positions quickly to avoid being exposed to unhedged overnight risk or excessive tracking error. Fishman also notes that Asset Managers and Institutions appear most at risk as they have recently started reporting short VIX futures positions. Perhaps we should just hope that there won’t be a negative market headline in the final minutes of any trading day anytime soon but should any of our readers wish to know the derivatives analyst would prepare for something jarring in the short term, Fishman suggests that client buy February 18-strike VIX call versus selling April 18-strike VIX calls with an intention to close the trade before the February 14 expiry. Read more At the same time, Bloomberg also reported that the 50-cent VIX player started buying short-dated options This entailed buying back 262,500 January VIX puts with a strike price of 12, selling 262,500 15 calls, and buying back 525,000 25 calls in order to close out the existing position. Then, the new position was established by selling 262,500 12 February puts, buying 262,500 15 calls, and selling 525,000 25 calls. While the ‘Elephant’ originally traded three-month options, rolling after two months, they appear to have switched to a one-month cycle More generally, the ‘Elephant’ trades reflect a trend towards low premium outlay hedges with minimal convexity,” the strategist concludes. “Clients we talk to have been more interested in VIX call flies or S&P put flies that carry well and have a fairly low initial cost, but may not mark up as much as an outright option in a risk-off scenario. Read more You can invest in volatility ETPs, but be prudent and hedge the risks accordingly. ByMarketNews Published via http://harbourfronttechnologies.blogspot.com/
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On this last day of 2017, we are going to list some of the most important lessons of the year.
In May, Paul Singer of Elliott Management laid out some of his major investment lessons in his letter to investors. In our opinion, the followings are the most important:
Click here to watch Paul Singer’s Strategy for Successful Investing Elliott Management Founder and Co-CEO Paul Singer discusses his investment technique as trying to “make money as close as possible to all the time.” He also talks about why his strategy for holding Argentina bonds paid off so well. He speaks to David Rubenstein on “The David Rubenstein Show: Peer-to-Peer Conversations.” Click here for more interviews. ByMarketNews Published via http://harbourfronttechnologies.blogspot.com/ In the previous post, we looked at some statistical properties of the empirical distributions of spot SPX and VIX. In this post, we are going to investigate the mean reverting and trending properties of these indices. To do so, we are going to calculate their Hurst exponents. There exist a variety of techniques for calculating the Hurst exponent, see e.g. the Wikipedia page. We prefer the method presented in reference [1] as it could be related to the variance of a Weiner process which plays an important role in the options pricing theory. When H=0.5, the underlying is said to be following a random walk (GBM) process. When H<0.5, the underlying is considered mean reverting, and when H>0.5 it is considered trending. Table below presents the Hurst exponents for SPX, VIX and VXX. The data used for SPX and VIX is the same as in the previous post. The data for VXX is from Feb 2009 to the present. We display Hurst exponents for 2 different ranges of lags: short term (5-20 days) and long term (200-250 days).
We observe that SPX is mean reverting in a short term (average H=0.45) while trending in a long term (average H=0.51). This is consistent with our experience. The result for spot VIX (non tradable) is interesting. It’s mean reverting in a short term (H=0.37) and strongly mean reverting in a long term (H=0.28). As for VXX, the result is a little bit surprising. We had thought that VXX should exhibit some trendiness in a certain timeframe. However, VXX is mean reverting in both short- and long-term timeframes (H=0.46). Knowing whether the underlying is mean reverting or trending can improve the efficiency of the hedging process. References [1] T. Di Matteo et al. Physica A 324 (2003) 183-188 Post Source Here: Mean Reverting and Trending Properties of SPX and VIX The sell-off in the high yield bond Exchange Traded Funds space last month reminds us of an important risk factor: liquidity. But what exactly is liquidity risk? According to Aleksander Kocic, derivatives strategist at Deutsche Bank AG, Liquidity transforms the risk of default (the ability that the debtor may not be able to pay back his debt) into the risk that the securities representing the debt find no purchasers ... today’s era of booming bond sales has an eerie parallel to the subprime crisis of the mid-2000s. Back then, low interest rates spurred an intense search for yield that culminated in investors purchasing risky home loans in the form of securitized and salable bonds. Such securitizations had the benefit of convenience as investors could buy and sell specific exposures comprising hundreds of thousands of individual home loans. The forced unwind of leverage was responsible for the transformation of conditional insolvency to unconditional illiquidity. Read more [caption id="attachment_436" align="aligncenter" width="561"] With the recent proliferation of Exchange Traded Funds, there is no surprise that there exist ETFs that are supposedly designed to offer “liquidity transformation”, i.e. they would allow investors to buy and sell illiquid debt instantaneously. However, liquidity risk is still there, and those ETFs can actually exacerbate the risk. As for now, an important question to ask is: was the liquidity risk priced in? According to John Davi on Valuewalk, it is not, and 2018 can see an increase in liquidity risk. The markets, however, trade on the margin and 2018 will begin to see liquidity decline in the US. The Fed has started to raise rates, wants to hike more, and quantitative tightening will further reduce liquidity. The repercussions are quite significant – especially on the margin. It is not surprising that liquidity sensitive asset classes such as US high yield credit, US Small Caps, and Japan corrected in October/November. Historically, liquidity in capital markets starts to decline in Q4 as banks begin to wind down their balance sheet ahead of year end. Plus, we have the potential for another Fed rate hike in December. The “liquidity based correction” was likely in anticipation of both events. Read more If liquidity deteriorates, portfolio managers can use liquid credit and/or volatility derivatives to hedge the risks. Originally Published Here: Liquidity Risk and Exchange Traded Funds Robert James Shiller is an American Nobel Laureate, economist, academic, and best-selling author. He currently serves as a Sterling Professor of Economics at Yale University and is a fellow at the Yale School of Management's International Center for Finance. Shiller has been a research associate of the National Bureau of Economic Research (NBER) since 1980, was vice president of the American Economic Association in 2005, and president of the Eastern Economic Association for 2006–2007. He is also the co‑founder and chief economist of the investment management firm MacroMarkets LLC. Read more
Tommy Atlee '20 sits down with Economics Professor Robert Shiller, 2017 Truman Medal recipient and 2013 Nobel Prize in Economics Laureate, to talk about his background in economics and his thoughts for the future.
Click here to watch the interview
Click here for more interviews.
ByMarketNews
Published via http://harbourfronttechnologies.blogspot.com/ VIX related products (ETNs, futures and options) are becoming popular financial instruments, for both hedging and speculation, these days. The volatility index VIX was developed in the early 90’s. In its early days, it led the derivative markets. Today the dynamics has changed. Now there is strong evidence that the VIX futures market leads the cash index. In this post we are going to look at some statistical properties of the spot VIX index. We used data from January 1990 to May 2017. Graph below shows the kernel distribution of spot VIX. [caption id="attachment_313" align="aligncenter" width="564"] It can be seen that the distribution of spot VIX is not normal, and it possesses a right tail. We next look at the Q-Q plot of spot VIX. Graph below shows the Q-Q plot. It’s apparent that the distribution of spot VIX is not normal. The right-tail behavior can also be seen clearly. Intuitively, it makes sense since the VIX index often experiences very sharp, upward spikes. [caption id="attachment_314" align="aligncenter" width="564"] It is interesting to observe that there exists a natural floor around 9% on the left side, i.e. historically speaking, 9% has been a minimum for spot VIX. We now look at the distribution of VIX returns. Graph below shows the Q-Q plot of VIX returns. We observe that the return distribution is closer to normal than the spot VIX distribution. However, it still exhibits the right tail behavior. [caption id="attachment_315" align="aligncenter" width="564"] It’s interesting to see that in the return space, the VIX distribution has a left tail similar to the equity indices. This is probably due to large decreases in the spot VIX after sharp volatility spikes. The natural floor of the spot VIX index and its left tail in the return space can lead to construction of good risk/reward trading strategies. Originally Published Here: Statistical Distributions of the Volatility Index Peter Carr recently gave a talk on volatility trading at the Fields institute. Summary: In general, an option’s fair value depends crucially on the volatility of its underlying asset. In a stochastic volatility (SV) setting, an at-the-money straddle can be dynamically traded to profit on average from the difference between its underlying’s instantaneous variance rate and its Black Merton Scholes (BMS) implied variance rate. In SV models, an option’s fair value also depends on the covariation rate between returns and volatility. We show that a pair of out-of-the-money options can be dynamically traded to profit on average from the difference between this instantaneous covariation rate and half the slope of a BMS implied variance curve. Finally, in SV models, an option’s fair value also depends on the variance rate of volatility. We show that an option triple can be dynamically traded to profit on average from the difference between this instantaneous variance rate and a convexity measure of the BMS implied variance curve. Our results yield precise financial interpretations of particular measures of the level, slope, and curvature of a BMS implied variance curve. These interpretations help explain standard quotation conventions found in the over-the counter market for options written on precious metals and on foreign exchange. In this talk, Carr discussed which options you should trade when
Click here to watch Article Source Here: Volatility, Skew, and Smile Trading
Factor investing is becoming popular these days. It has its roots in Arbitrage Pricing Theory. According to Wikipedia
Arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly—the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line. S. Ross is the Father of Arbitrage Pricing Theory. D. Musto of Wharton recently summarized the key points of Arbitrage Pricing Theory in this podcast
This is a very elegant way to price the whole range of derivative securities out there. So Steve, building on the work of [Fisher] Black and [Myron] Scholes, showed how you could take what they did and think about it as a binomial framework that would help you price a wide range of securities, and show you how you go about replicating the payoff of any derivative security you might be interested in, with this binomial trading technique. ByMarketNews Published via http://harbourfronttechnologies.blogspot.com/ Value at Risk (VaR) is an important risk measure that large financial institutions use for managing the risks and allocating capital. Wikipedia defines VaR as follows: Value at Risk (VaR) is a measure of the risk of investments. It estimates how much a set of investments might lose, given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses. For a given portfolio, time horizon, and probability p, the p VaR can be defined informally as the maximum possible loss during the time if we exclude worse outcomes whose probability is less than p. This assumes mark-to-market pricing, and no trading in the portfolio.
Bloomberg recently reported that the combined VaR of the six largest US banks has decreased from $1 billion in 2009 to $279 million. Does this mean that we have much less risk now than before? Not so if we adjust for the decreasing trend in volatility What if we strip it out to get a sense of whether risk-taking has really declined, independent of the broader market? The result won’t be perfect, 3 but it should give us a rough idea. It indicates that, relative to the broader market, the banks’ trading operations are only about 25 percent less risky than they were in 2009 -- and have actually become a bit riskier over the past year. Read more In a similar context, Peter Guy pointed out that, generally speaking, risk models are vulnerable because they were developed and tested in a market environment that can change in the future ... risk models are vulnerable because a decade of zero interest rates have never occurred before in financial and economic history. No one possesses accurate historical data to predict the future. And quantitative models and algorithms heavily depend on historical data for forecasting risk. “There are no models that are able to accurately capture the effect of rising interest rates. You need to reach back to the period before quantitative easing began,” Read more So what are the solutions? One solution is to develop stress scenarios, then use them to calculate probability-weighted, forward-looking risk measures. Additionally, we can implement other VaR variants that better account for the tail risks. Article Source Here: Is Value at Risk a Good Risk Measure? This post is the continuation of the previous one on the riskiness of OTM vs. ATM short put options and the effect of leverage on the risk measures. In this installment we’re going to perform similar studies with the only exception that from inception until maturity the short options are dynamically hedged. The simulation methodology and parameters are the same as in the previous study. As a reference, results for the static case are replicated here:
Table below summarizes the results for the dynamically hedged case
From the Table above, we observe that:
It is important to note that given the same notional amount, a delta-hedged position is less risky than a static position. For example, the VaR of a static, cash-secured (m=100%) short put position is 0.194, while the VaR of the corresponding dynamically-hedged position is only 0.0073. This explains why proprietary trading firms and hedge funds often engage in the practice of dynamic hedging. Finally, we note that while Value at Risk takes into account the tail risks to some degree, it’s probably not the best measure of tail risks. Using other risk measures that better incorporate the tail risks can alter the results and lead to different conclusions.
Originally Published Here: Are Short Out-of-the-Money Put Options Risky? Part 2: Dynamic Case |
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HYG High Yield Bond ETF as at Dec 22, 2017. Source: Interactivebrokers[/caption]
Kernel distribution of the spot VIX index[/caption]
Q-Q plot of spot VIX vs. standard normal[/caption]
Q-Q plot of VIX returns vs. standard normal[/caption]
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