05 February 2021

# Valuation and Risk Analysis of Cryptocurrency Options

Crypto Currencies have received a great deal of attention recently, mostly due to Bitcoin's impressive rally over the last few months. As the global crypto market gains wider acceptance, investors and speculators alike are increasingly trading derivatives in order to both manage risk and gain exposure to crypto currency volatility.

Currently, several global venues now offer futures contracts, allowing traders to establish both long and short linear exposure to Bitcoin (such as the CME and ICE futures exchanges) without having to physically posses or deal in the currency in question, as these contracts cash-settle in traditional currencies. Such exchanges now also offer options on futures, providing market participants with non-linear hedging and speculation alternatives as well. Internationally, venues exist for direct crypto currency options that both trade and settle in the reference crytpo coin rate (such as Bit.com and Derebit). A trader could therefore establish a purely crypto-currency option hedging position, unexposed to any standard currency rate.

Independent valuation and analysis of such positions is crucial, as portfolio managers may hold direct crypto currencies, options, and futures, across several venues, making a single, unified view of portfolio risk all the more necessary.

The RiskAPI system provides users with valuation and analysis of spot crypto currencies, futures, options on futures, as well as direct options on crytpo currencies. Using the system's options on currencies notation, the example below shows a range of strikes for some near-term call options along with their associated risk and valuation measures:

The symbols in the example above leverage a formulaic symbol format within RiskAPI allowing users to specify individual option terms as well as underlying currency exchange rates (in this case USDBTC). The set of calculations provide for both point-in-time valuation, as well as statistical analysis of simulated (or historical) returns, depending on the VaR model chosen (in this case Monte Carlo)

For derivatives settling purely in BTC (and others), the ability to change the calculation base currency allows for views of exposure purely in the crypto currency of choice. In the above example, the same call options are stressed under a multi-dimensional spot and implied volatility shock, with the results (Stress Impact) shown in Bitcoin, with no USD exposure or value involved.

04 December 2020

# Managing Natural Gas Risk With Volatility Adjusted Futures

As winter approaches in the northern hemisphere, the potential for outsized moves in global natural gas markets increases. These can take place due to either unexpected cooling or warming periods which may significantly affect consumer demand and produce large changes in natural gas prices.

In general, price dynamics in natural gas markets are uniquely challenging for portfolio and risk managers. This is partly because of the difficulty in forecasting weather but also since natural gas volatility tends to increase quite dramatically as actively trading futures contracts become "prompt" (i.e., as they approach their delivery dates). The historical returns for a given contract may be well-behaved and adhere to expected volatility estimates throughout the contract's trading life. However, as the delivery date of the contract approaches and it becomes prompt, volatility tends to explode higher, rendering any historical-data driven analysis quite unpredictive and falling well short of correctly estimating the magnitude of future returns.

This effect on volatility is demonstrated quite well by the behavior of the most recent front contract for the NYMEX Henry Hub Natural Gas future. Henry Hub Natural Gas is a monthly futures contract that expires in the final trading days prior to each delivery month. There are 12 contracts that trade for each calendar year, each with its own delivery date at or near contract expiry. This highly liquid contract trades several years out into the future, providing a very efficient price discovery, speculation, and hedging mechanism for the US natural gas markets. The December 2020 future, for example, was the prompt contract during the entire month of November 2020:

As can be seen above, the realized volatility of this contract remains fairly range-bound for most of the calendar year 2020. However, as the contract approaches the prompt month (expiration at the end of November), we see an effective doubling of volatility, from 21% in September to almost 40% by contract expiration on November 25th, 2020. Applying a statistical estimate such as Value at Risk (VaR) to this contract's data would vastly underestimate exposure prior to the prompt period. The problem mainly arises from the desire to include more data in a given statistical analysis, yet when included, this data has the effect of underestimating future exposure since it mostly contains returns observations from a vastly lower risk regime (i.e. all the historical returns preceding the prompt period).

The effect is greatly pronounced when looking at VaR during the prompt month itself, specifically during two dates: November 3rd and November 16th. Two commonly used VaR models, Parametric (also known as delta-normal) and Historical Simulation, both vastly underestimate actual return magnitudes on both of these days:

Here we see traditional approaches to VaR performing quite badly, with 99% confidence, 1-day VaR estimated using 1 year of data up to and before each date (t-1), falling well short of the actual P&L for a single long contract of NGZ20. 99% Confidence Parametric VaR as of 11/2/2020, for example, estimates a maximum loss of $1,1920, (a 3.18% return), while the actual loss on 11/3 was $1,850 (or -5.70%). The outsized loss on 11/16 far exceeds both methods of risk estimation, with Historical Simulation VaR, even as the better of the two methods, still coming short by more than a factor of 2.

As a remedy to this problem, RiskAPI includes Volatility-Adjusted Futures (VAF's), a class of mathematically constructed futures contract data that utilizes historical returns combined with measurements of recent volatility to normalize past returns to current volatility conditions. The idea behind this construct is to preserve the statistical significance of historical returns, while making them relevant to present day market conditions, specifically with regards to current volatility. In short, the construct allows users to take advantage of large amounts of historical return observations and to simulate these returns behaving as if they took place under similar, present day volatility conditions.

The RiskAPI system provides a simple format for converting any futures contract to use this volatility sampling and normalization process in order to seamlessly adjust historical returns. For the December 2020 Henry Hub Natural Gas contract, symbol: NGZ20, a symbol modification is applied by adding a hash sign to this code: NGZ20#. This prompts the system to modify the historical returns of this contract by normalizing historical return observations to present day volatility conditions using past and present volatility measurements.

Using the RiskAPI Add-In, which provides a simple keyword-based mechanism to quickly generate VaR in Excel via the RiskAPI cloud service, we reproduce the same calculations, this time on the VAF version of the Henry Hub contract, NGZ20#:

The result is a much better-performing estimate of losses, using only data preceding each outsized return event:

Additional manipulations of returns are available, allowing users to take advantage of filtered, seasonal samples, i.e., constructing a set of normalized returns sampled from specific months out of each year, going back several years (a full whitepaper of this methodology exists for registered and trial users of the system).

20 October 2020

# Factor Analysis Part II

In Part I of this series, we explored the ability to calculate portfolio factor sensitivities using the RiskAPI Add-In. In Part II, we will look at the application of a multi-factor portfolio stress test using the same principles.

Using the Stress-Testing feature of the RiskAPI Add-In, we can set up a multi-factor stress test, applying shocks of varying magnitudes and directions to each factor of interest. The system will evaluate the simultaneous effects of such a shock scenario both on each individual component as well as the portfolio as a whole.

As in Part I, we continue to leverage the "Market Macro" keywords-based feature of the Add-In to quickly generate RiskAPI calculations on portfolio and factor symbols and quantities. The above image shows the output of a multi-factor stress test performed on all 103 Nasdaq 100 components against the same factors used in Part I. These are presented again here:

- VLUE - the value factor
- QUAL - the quality factor
- MTUM - the momentum factor
- SIZE - the small cap factor
- STLG - the growth factor

The "Index" and "Index Stress" keywords allow us to specify which set of factors the stress test is being run with, as well as the magnitudes of the shocks applied to each factor. The "Stress Type" keyword defines, via the entry "Index MR", that a multi-factor stress test is being performed (also available are single-factor, underlying prices, implied volatility, and other types). The Index MR stress testing method leverages the system's multiple regression capability to calculate the portfolio's factor sensitivities over the data set and factors specified. It then applies the individual user-defined factor shock values in the process of evaluating the multi-factor shock scenario.

For the stress test in question, the large one-day changes in value experienced on March 16th, 2020 are used. These ranged from -12% in the SPX to as high as 14.6% in the SIZE factor. The system returns three pieces of information as outputs of the scenario:

- Stress Price - the price of the portfolio component under the shock scenario
- Stress Impact - the simulated P&L of the portfolio component under the shock scenario
- Total Stress Impact - the total portfolio simulated P&L under the shock scenario

The same process can be applied to a less intuitive portfolio, leveraging the options valuation capabilities of the system:

Here we see the same multi-factor scenario applied to a present-day "costless-collar" options strategy on AAPL shares. The system automatically performs the factor sensitivity analysis, shock-propagation, and options valuation required to evaluate such a scenario on the option portfolio in question.