Consider a derivative V(S t ,r t ,t) dependent on the (nondividend paying) stock price S t and short rate r t with SDEs given by dS t (t)S t dt S t dW t and dr t ((t) r t )dt dU t respectively with dW t dU t pdt Using a hedging argument (say with a stock and a discount bond), find the PDE for V(S t...

Heres the derivation of the PDE for VSt rt t using a hedging argument with a stock and a discount bo ...

Consider a derivative V(S t ,r t ,t) dependent on the (nondividend-paying) stock price S t and

Question:

Consider a derivative V(S_t,r_t,t) dependent on the (nondividend-paying) stock price S_tand short rate r_t with SDEs given by dS_t = μ (t)S_tdt + σS_tdW_t and dr_t = κ(θ(t) – r_t)dt + λdU_trespectively with dW_tdU_t= pdt. Using a hedging argument (say with a stock and a discount bond), find the PDE for V(S_t, r_t, t).