| On the basis of nearly five Nobel Prize winners' work, such as CAPM and APT, very technical Mathematical tools come into the field of Financial world. 1973 is a very meaningful year, Black and Scholes published their paper of Option pricing which won the Nobel Prize, at the same year, Chicago Stock Exchange opens the Option trade. These started the most important innovation, and the revolution of Wall Street. The essence of the revolution is asset pricing, including Option pricing and interest rate modelling.Asian Options are path-dependent exotic Options, their values depend on the average value of the original assets in the periods. As first introduced in Tokyo, Japan, they got the name of Asian Options. The first paper to discuss Asian Options academically is Boyle and Emanuel(1980). Vorst(1996) had a review of research results of Asian Options.We first show the Partial Differential Equations method and the Probability method to price Asian Options. The PDE method which is known is mainly from Jiang(2003). We are interested in the more realistic condition, which is the pricing formula for Geometric Asian Options under stochastic interest rates. Specifically, We firstly use the Ho-Lee model of instantaneous interest rate, we use PDE method to give the pricing model, and use Probability method to give a closed-form solution of floating and fixed strike Asian Options. Through introducing a new form and an inequality, we independently give a uniform solution of floating and fixed strike Asian Options. At last, we give the corresponding call-put parity. |
