"FIXED INCOME VERSUS EQUITY DERIVATIVES While the ideas behind pricing fixed income and equity derivatives are similar in many ways, there are important differences as well. In particular, it is worth describing why models created for the stock market cannot be adopted without modification for use in fixed income markets.
The famous Black-Scholes-Merton pricing analysis of stock options can be summarized as follows. Under the assumption that the stock price evolves according to a particular random process and that the short-term interest rate is constant, it is possible to form a portfolio of stocks and short-term bonds that replicates the payoffs of an option. Therefore, by arbitrage arguments, the price of the option must equal the known price of the replicating portfolio.
Say that an investor wants to price an option on a five-year bond by a direct application of this logic. The investor would have to begin by making an assumption about how the price of the five-year bond evolves over time. But this is considerably more complicated than making assumptions about how the price of a stock evolves over time. First, the price of a bond must converge to its face value at maturity while the random process describing the stock price need not be constrained in any similar way. Second, because of the maturity constraint, the volatility of a bond’s price must eventually get smaller as the bond approaches maturity. The simpler assumption that the volatility of a stock is constant is not so appropriate for bonds. Third, since stock volatility is very large relative to short-term rate volatility, it may be relatively harmless to assume that the short-term rate is constant. By contrast, it can be difficult to defend the assumption that a bond price follows some random process while the short-term interest rate is constant." -- Tuckman, Bruce; Serrat, Angel. Fixed Income Securities: Tools for Today's Markets (Wiley Finance) (pp. 225-226). Wiley. Kindle Edition.
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