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01 June 2021

Valuation and Risk Analysis of Accumulator Contracts

A commodity accumulator contract is a derivative product which allows producers to sell higher volumes of their product if the market price rises above a certain threshold. Grain farmers, for example, take advantage of these contracts to sell more of their crop (usually double the amount) if prices rise. Ultimately, the goal of entering into an accumulator is to sell more of a product at a higher price. As with all things in life, there is no such thing as a free lunch. Therefore, accumulators come embedded with a knock-out feature. If the given commodity price falls below the knock-out price, the entire contract becomes null and void. At this point, the producer is left to sell its remaining inventory at the prevailing lower market rates.

The typical accumulator is characterized by a Double-Up feature, an Accumulation Level, and a Knock-Out Level. The contract works as follows:

  1. Over the life of the contract, as defined by the start and expiration dates, if, at the time of expiration, the price of the underlying asset settles above the Knock-Out Level, but below the Accumulation level, the entire original contract quantity will be sold at the settlement price.

     

  2. If, at expiration, the price of the underlying asset settles above the Accumulation level, then twice the quantity will be sold at the Accumulation Level (the Double-Up feature).

     

  3. If the price of the underlying asset settles at or below the Knock-Out Level at any point during the life of the contract, the contract immediately cancels and is known as "Knocked-Out". Depending on the structure of the Accumulator, either some or all of the original contract quantity can then only be sold at current market rates.

Variations of the above terms also exist, such as a daily pricing, in which the Double-Up feature can come into play at any day during the life of the contract, rather than just at expiration (i.e. American vs. European-style).

Valuation:

An accumulator contract can be valued as a combination of barrier option puts and calls. A barrier option is a type of option that, in addition to having a strike, expiration, and exercise style, also includes barrier price. The barrier price, depending on the barrier type, can cause the option to become instantly worthless/valuable if the price of the underlying asset crosses it in some manner (i.e. down-and-out or up-and-in).

Valuation of an Accumulator contract requires capturing the three distinct behaviors defined previously:

  1. Sale of the original quantity at market rates above the Knock-Out level but below the Accumulation level: This can be accomplished by being short a call option and long a put option in a costless manner. A costless collar is entered into by selling a call and using the sale premium to purchase a put at a given strike where the put premium is equivalent to the call premium received. This strategy, known as a "costless collar", results in the underlying asset simply being exposed to market rates if its price is above the Put option strike and below the Call option strike. This combination also makes the Accumulator cost-free at initiation.

     

  2. The double-up behavior above the Accumulation level: This behavior can be replicated via using two short calls instead of one short call in the costless collar above and additionally setting the strike price of these to the Accumulation level. This is because, as a producer, being short a single call would require the sale of the underlying asset to a counter-party long the call at any price above the strike (Accumulation) price. By being short 2 calls, the producer would therefore be required to sell twice the underlying amount at prices above the strike price at the time call exercise. Note that the premium paid for the Put option purchased would need to be equivalent to the total premium from the sale of both call options.

     

  3. The Knock-out level: This behavior can be replicated using down-and-out Barrier options in all of the above, with the knock-out barriers of each set to the Knock-Out level of the accumulator contract for both the Put and the two short Calls. By setting the barriers to this level, the entire combination becomes worthless when the underlying asset price falls below the Knock-Out barrier.

     

Use in the RiskAPI System:

The RiskAPI service includes a valuation capability for Barrier puts and calls. A flexible format is available to specify both listed and OTC option contracts on commodities. Using this format, both European and American puts and calls can be specified. Additional terms exist in the format to allow specification of down-and-out Knock-Out barriers. Accumulator contracts can be replicated by providing the appropriate symbols and quantities for the required put and call options:

 

 

The CME Corn barrier option spread above illustrates the RiskAPI specification of an Accumulator contract created by combining two long Dec 2021 Barrier options struck at 770 and one short Dec 2021 Put struck at 610, each with a down-and-out Knock-Out barrier of 400. The combination of these contracts results in an Accumulator with the following characteristics:

  • Accumulation Level: 610
  • Double-Up Level: 770
  • Knock-Out Level: 400

Risk Analysis

The Accumulator can be easily risk analyzed via the RiskAPI system, as is the case with any valid symbol combination:

 

 

The above shows an example of a Monte Carlo VaR performed on the Accumulator, using the RiskAPI Add-In. Similarly, a 2-standard deviation shock to Corn prices can also be performed via the system's Stress Impact calculation:

 

 

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).

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