Interest Rates and Term Structure Models
The assumption made in the Black-Scholes world, in particular in the Black-76 model Equation 8.10, that interest rates are non-stochastic directly contradicts the very existence of interest rate options. If interest rates were deterministic and hence predictable with certainty for all future times, we would know at time t which options will be in or out of the money upon maturity T. The options which are out of the money at maturity would be worthless at all earlier times t < T as well. The options which are in the money at maturity would be nothing other than forward transactions. Thus, the assumptions made in pricing interest rate options using the Black-76 model imply that these very options should not even exist! In spite of this fact, the option prices obtained by applying the Black-76 model are surprisingly good. The results of recent research  have shown that the effects of several “false” assumptions (in particular, the assumed equality of forward and futures prices) tend to cancel out each other.1
KeywordsInterest Rate Discount Factor Forward Rate Martingale Measure Spot Rate
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