# Consider the following discrete version of the Vasicek model when the short rate r(t) follows the discrete

## Question:

Consider the following discrete version of the Vasicek model when the short rate r(t) follows the discrete mean reversion binary random walk

Let V (t) denote the value of an interest rate contingent claim at current time t,V_{u}(t + 1) and V_{d} (t + 1) be the corresponding values of the contingent claim at time t + 1 when the short rate moves up and down, respectively. Let B(t,T ) be the price of a zero-coupon bond that pays one dollar at time T and observe that B(t,t + 1) = e^{−r(t)}. By adopting a similar approach as the Cox–Ross– Rubinstein binomial pricing model, show that the binomial formula that relates V (t),V_{u}(t + 1) and V_{d} (t + 1) is given by (Heston, 1995)

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