Yesterday, a nondividend paying stock was selling for $40 and a call option on the stock was selling for $2.7804 and has 91 days left to expiration. The call option on the stock had a delta of 0.5824, a gamma of 0.0652, and a daily theta of 0.0173. Today, the stock trades for $39.25. The annual continuously compounded risk-free interest rate is 0.08. Find the new option price using the delta-gamma-theta approximation. [answer: $2.3446]

using

V (St , T th) V (S_t,T t)+(S_t , T t)+ .5 ² (S_t , T t)+h(S_t , T t)