Question
Use DerivaGem to check that equation (19.4) is satisfied for the option considered in Section 19.1. (Note: DerivaGem produces a value of theta "per calendar day." The theta in equation (19.4) is "per year.")
Step 1
1. These parameters include the strike price, the current stock price, the risk-free interest rate, the time to expiration, and the volatility. Once we have these parameters, we can input them into DerivaGem to calculate the theta value per calendar day. Show more…
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For the initial conditions $\theta=\theta_{0}, \theta=0$, show that the constants $A$ and $B$ in equations (18.6) and $(18.7)$ are as given in (18.8). Hints: Show that $d \theta / d u=0$ if $\theta=0$. In equations (18.6) and ( $18.7)$, set $\theta=\theta_{0}$ and $d \theta / d u=0$ when $u=u_{0}$ and solve for $A$ and $B$. Then use the formula in Problem 5 to simplify your results to get equation (18.8).
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