Calculates swaption price in Vasicek Model using Joint simulation of (int_0_T(r(t)),r(T)) where T : Option Maturity r(t) : sport rate at time t in risk neutral measure int_0_T(r(t)) : integral of r(t) taken from time 0 to option maturity
Algorithm: 1.Calculate expected values of r(T) and integral_r(T) 2.Calculate correlation of r(t) and integral_of_r(t) using formulas for variances and covariance 3.Calculate fair rate for forward rate swap 4.Set swaptionstrike=fair rate (assume ATM swaption) 5.Calculate fixed leg payments vector using swaptionstrike 6.Start simulations For each simulation: 6a. Draw 2 random no. variables 6b. Transform the variables to make them correlated 6c. Simulate r(T) and integral_of_r(T) 6d. Calculate discount bond prices using simulated r(T) 6e. Calculate present value of fixed leg payments using discount factors in 6d 6e. Calculate swaption payoff using sum of fixed leg payments 6f.Discount option payoff using simulated integral_of_r(T) Repeat 6a.
Average PVs to get swpation price
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