Pricing of Quanto power options and related exotic options

The objective of this work is threefold. Firstly, to derive the no-arbitrage premium of the α-Quanto option with power type payoff. Secondly, to price the Quanto option of power payoff when the underlying foreign currency is driven by Brownian motion and Poisson jumps, via risk-neutral probability measure. Thirdly, derive and analyze the price of the compound call option contingent upon the Quanto power call option. Our approach in deriving the pricing formulas in all three cases would be probabilistic, based on the Feynman–Kac formula.