A stock is currently selling for $40. The stock pays no dividends. Given that the volatility relevant for the Black-Scholes equation is 30% and the continuously compounded risk-free interest rate is 8%. Consider a $40-strike purchased call on the stock with time to expiration in 6 months. What are the theta, rho, and psi?[answer: = 0.0136, = 0.1024, = 0.1232 ]

Where

= V/

Call = (T t)Se^{(T t)}N(d₁) and Put = (T t)S^{e(T t)}N(d₁)

= V/r

Call = (T t)Ke^{r(T t)}N(d2)

= V/t

d₁ =[ln(St/K) + (r + 0.5²)(T t)]/ [(T t)]

d₂= d₁ (T t)

V C(S, t) = Se^{(T t)}N(d₁) Ke^{r(T t)}N(d₂)

V P (S, t) = Ke^{r(T t)}N(d₂) Se^{(T t)}N(d₁)