Pricing of European options when the underlying stock price follows a linear birth–death process

This investigation considers a possible approach to price options if the underlying stock jumps up or down or remains unchanged, extending ideas of Cox and Ross to a more general jump model with state-dependent jump intensities. Provided that in addition to the stock itself one option on this stock is traded in the market, we can show by valuation of arbitrage arguments that the price of European options is then determined uniquely.