Derivatives
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Also, the relationship between the option price and the underlying price is not linear. Gamma determines the degree of curvature of this relationship. It is the second derivative that affects the option price’s sensitivity when the stock price changes over a wide range. (For small changes, delta is sufficient, because the curvature does not have…
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Trading options requires risk hedging.Suppose an investment fund uses the Black-Scholes-Merton model to calculate the value of a call option and then sells it in the market at a higher price. In substance, it has made a profit, but this profit is not yet realized because the option has not expired. For example, let’s assume…
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Black’s brilliant model was originally developed for pricing European futures options (“The Pricing of Commodity Contracts,” Journal of Financial Economics, 3 (March 1976)). Later, it turned out to be very convenient in practice for spot options as well. The main assumption of the model is that, in a risk-neutral world, futures prices evolve in the…
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Valuation of American-Style Futures Options using Binomial Trees American-style futures options are valued using binomial trees. The difference between a futures option and a stock option is that exercising a futures option does not require an upfront payment to enter into the futures contract. To illustrate with a simple one-step binomial tree, we first need…
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A futures option is the right, but not the obligation, to enter into a futures transaction at a predetermined futures price, by a predetermined date. The final date is usually set a few days before the expiration of the underlying futures contract (although there are exceptions for some financial assets). Futures options are mostly American-style.…
