Time to Manage Your Risk

Articles tagged with: Stress-Testing

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).


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:



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:

  1. Stress Price - the price of the portfolio component under the shock scenario
  2. Stress Impact - the simulated P&L of the portfolio component under the shock scenario
  3. 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.