LECTURER\'S QUESTION Describe two problems in using the Black option on futures

Question

LECTURER'S QUESTION

Describe two problems in using the Black option on futures pricing model for pricing options on Eurodollar futures.

MY ANSWER

1.         The Black-Scholes model assumes unrealistically that short-term interest rates constant.

2.         The model assumes that the variance of returns on the bond is constant over time. In fact, the variance may increase in the initial life of a bond, but it must decrease during the final stages of the bond’s life because the bond must trade at par at maturity. The decrease in variance of returns over the final portion of a bond’s life is called the pull-to-par.

CLASSMATE COMMENT

It looks like you were looking at the Black-Scholes model rather than the Black model which is a variation of Black-Scholes for pricing European options on futures. The problems may be similar though - I know the Black model also assumes a constant interest rate, but I am not sure if your second point is also a problem with the Black model.

PLEASE CAN YOU DEFEND MY ANSWER TO CLEAR MY CLASSMATE QUESTION PLEASE

Explanation / Answer

The Black-Scholes model makes certain assumptions, including:

Some of the assumptions in the formula are questionable under today’s economic and market conditions. For example, the calculation uses an assumed risk-free interest rate to compare to buying or selling options. It is questionable whether such a rate exists today.

The formula is also based on European-style options, those that can be exercised only on the last trading day. Other than some index options, the majority of publicly traded options can be closed at any time before expiration; this changes the calculation. Finally, the Black-Scholes model makes one assumption that is fatally flawed: the assumption is that implied volatility on the date of the analysis will remain unchanged until expiration. Every trader knows this is simply inaccurate.

'Black's Model'

A variation of the popular Black-Scholes options pricing model that allows for the valuation of options on futures contracts. Black's Model is used in the application of capped variable rate loans, and is also applied to price derivatives, such as bond options and swaptions.

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