Valuing an American Call on a Futures Contract with a Binomial Tree
Summary
The document presents a binomial pricing exercise for an American call option whose underlying is a futures contract. The stock tree is calibrated to a Black–Scholes geometric Brownian motion setup, while the option expires before the futures contract itself. The central modeling point in the accepted response is to build the stock tree, determine the futures price at the option’s expiration, and use that future value when working backward through the option valuation.
The prompt asks for the fair value and earliest possible exercise period, but the supplied response does not give either result or show a complete lattice calculation. A follow-up comment questions the probability multiplier used in a futures lattice, suggesting that calibration details remain unresolved in the excerpt. Thus, the document offers a useful framing for separating option maturity from futures delivery maturity, but it is not a worked solution and does not establish an exercise recommendation.
Key ideas
- The option expires before the futures contract, so the two maturities must be represented separately.
- A binomial stock tree can provide the underlying states used to construct futures values.
- The accepted response proposes calculating the futures price at option expiry before valuing the option backward.
- The excerpt does not provide the fair value, an exercise date, or a complete lattice calculation.
- A comment raises an unresolved question about the probability multiplier used in the futures lattice.
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Full text
# Options pricing exercise - American call option on a futures contract # Options pricing exercise - American call option on a futures contract I am confused by a particular exercise I am doing right now, I am hopeful that someone can walk me through as to how to solve it. I further hope the question is not considered too basic for this forum. Build a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with: T=.25 years, S0=100, r=2%, σ=30% and a dividend yield of c=1%. Compute the fair value of an American call option with strike K=110 and maturity n=10 periods where the option is written on a futures contract that expires after 15 periods. The futures contract is on the same underlying security as described in the previous questions. What is the earliest time period in which you might want to exercise the American? So what I would normally do to compute the value is to build a lattice and then work backwards in order to see what the value is. Yet the part with "where the option is written on a futures contract that expires after 15 periods", leaves me awfully confused as to what I should be doing as well as what implications that has for the exercise. Thank you for any feedback! [at this point I found the solution, big thanks to all the contributors, I deleted the lattices in order not to misguide anyone as they clearly did produce the wrong result] ## Answer by roym00 (score 0, accepted) https://quant.stackexchange.com/a/21266 You can build the binomial tree for the stock. After ten periods, the option expires and you enter in the future contract at a certain future price (noob2 gave a big help on this): you compute the future price at period 10 and then you work backwards for the option valuation. ## Answer by NDC (score 0) https://quant.stackexchange.com/a/21673 Noir : I'm studying the same coursera course as you and wonder why you used a multiplier "q" = 0.7483 in calculating the futures lattice eg first row of second column from left 175.42 = 0.7483 * 178.77 + (1-0.7483) * 165.45 and not the calculated value of q equal to 0.4925.
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