Jump Diffusion Price Process and Risk Hedge Strategy

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For the passive risk hedge strategy, we present the construction method of an index-fund in the world of continuous time and the stock price with jumps. To hedge the price evolution at a sudden rise or crash of stock and commodity markets, we present a mathematical model. Under this model, we derive the valuation formulas for European call option and exchange option. A put-call-parity between the exchange call option and the put option is provided.