- Mathematical Finance Lecture Note 1 Positive Interest Rate Model Suppose That Present Value Evaluation Under The Equi 1 (42.11 KiB) Viewed 31 times
Mathematical Finance Lecture Note 1. (Positive interest rate model) Suppose that present value evaluation under the equivalent martingale measure was expressed under the market observed measure as such [efx/0,- *x,10. –É[1,x,1%.] klor = (1.1) efel ex. o. - Ep. 8, 101 X, (1.2) Ē[] Arrow-Debreu price n, is defined from a potential , as n = 1 +S,902, (1.3) (1) Compute expressions for pure discount bond, instantaneous forward rate, and risk-free short rate (2) (Flesker-Hughston) Let Arrow-Debreu price be 11. = G,COM,+G(1) where an exponential martingale M, has usual properties. M, = E[M,10,]20 M = 1 (1.5) This case, what would become pure discount bond, instantancous forward rate, and risk-free short rate? (3) Study a concrete example, g(t)= a(0,1)D(0,1) M, - Stare (1.6) dw, -N(0, dt)