These are financial math problems.

1. Consider the payoff function: K+K,- K -S ,0 O be the spot price of the stock at current time t O be the spot at time t 0. (b) A(S) = (K - $), with constants a 70, K > 0. 3. Consider the standard up-and-in call and up-and-in put barrier options with common strike K> 0 and barrier level B > 0. Obtain a put-call parity relation between the pricing functions, CUT, S, K; B) and pul (T,S, K;B), for these two barrier options, where 1 > 0 is the time- to-maturity. 4. Consider a binary-on-a-forward compound option on the stock with outer and inner payoff functions defined respectively by 0(1)(c) := If 0, with respective maturities Ti and T2 and fixed strikes Ki >0, K2 > 0. Determine the time-t no-arbitrage pricing formula V (t, S) = V(t, S:T ,T2), t O be the spot price of the stock at current time t O be the spot at time t 0. (b) A(S) = (K - $), with constants a 70, K > 0. 3. Consider the standard up-and-in call and up-and-in put barrier options with common strike K> 0 and barrier level B > 0. Obtain a put-call parity relation between the pricing functions, CUT, S, K; B) and pul (T,S, K;B), for these two barrier options, where 1 > 0 is the time- to-maturity. 4. Consider a binary-on-a-forward compound option on the stock with outer and inner payoff functions defined respectively by 0(1)(c) := If 0, with respective maturities Ti and T2 and fixed strikes Ki >0, K2 > 0. Determine the time-t no-arbitrage pricing formula V (t, S) = V(t, S:T ,T2), t