Equal risk pricing and hedging of financial derivatives with convex risk measures

In this paper, we consider the problem of equal risk pricing and hedging in which fair price an option is that exposes both sides contract to same level risk. Focusing for first time on context where measured according convex measures, establish reduces solving independently writer buyer's problems with zero initial capital. By further imposing measures decompose a way satisfies Markovian property, provide dynamic programming equations can be used solve European American options. All our results are general enough accommodate situations worst-case measure, as typically done robust optimization. Our numerical study illustrates advantages over schemes only account single party, based quadratic (i.e. ?-arbitrage pricing), or fixed equivalent martingale measure Black–Scholes pricing). particular, confirm when employing buyer end up being exposed risks more similar average smaller than what they would experience other approaches.