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Hard · Stochastic Calculus · Quant Trader interview question · put-call parity, symmetry, black-scholes, options
Consider a simplified Black-Scholes world where the risk-free rate $r$ and the dividend yield $q$ are both zero. You observe a European call option with a strike price of $K$ trading on an underlying asset with a spot price of $S$. You also observe a European put option. What is the relationship between the price of the call, $C(S, K)$, and the price of the put, $P(K, S)$? In other words, how does the price of a call with strike $K$ on an asset at $S$ relate to the price of a put with strike $