Derivation of the Black-Scholes Formula for Pricing European Call Options under Unknown Interest Rates
Date
2013
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Bryn Mawr College. Department of Mathematics
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Thesis
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Award
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eng
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Abstract
This paper investigates the fair price of European call options under the Black-Scholes model. The original model proposed by Black and Scholes (1973) priced European call options under five basic assumptions, namely that stock prices follow Geometric Brownian motion, stock pays no dividends during the option’s life, markets are efficient, no commissions are charged, and that interest rates remain constant and known. This paper relaxes the assumption that interest rates remain constant and known and derives the fair price formula for a European call option assuming that the present interest r1 is constant and known, while the future interest rate r2 is constant but unknown.