Convertible Bonds Binomial Model • The price of the option will be:
1 2 2 C= × [ p × max( 0 , u S − K) 2 (1 + r ) + (1 − p ) 2 × max(0, d 2 S − K ) + 2 × p × (1 − p ) × max(0, udS − K )]
• There are “two paths” that lead to the intermediate state (that explains the “2”) • Suppose we know the volatility σ and the time to maturity t, we can retrieve u and d (see B&S)
u=e
σ t/n
; d = 1/ u