# Questions tagged [put-call-parity]

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### Understanding basic options arbitrage in Hull

I’m reading Hull’s book, Options, Futures and Other Derivatives. In Chapter 11 he discusses put-call parity and the arbitrage opportunities that can result from its violation. I’m having a basic issue,...
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### Upper bound for difference of two call options

Let $r>0$ be the interest rate and $S_t$ the price of a stock at time $t$. Let $C(t,K_1),C(t,K_2)$ be the price of call options at time $t$ with the same underlying asset $S$, the same maturity $T$ ...
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### Proof of the put-call parity formula

I just learned about the put-call parity formula and read the proof of it, which goes as follows. Put-call parity formula: Let $C,P$ denote respectively the prices of a call and a put, both of ...
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### How does a stock becoming hard to borrow affect puts and calls?

Here is my understanding from what I’ve gathered, but I want to confirm if this is correct (and/or if there’s something I’m missing). If a stock becomes hard to borrow, one can create a synthetic ...
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### Why does the risk-free rate implied by put-call parity vary with strike prices?

Suppose I do the following: buy one lot of some underlying stock currently trading at price $S$, write a call with strike price $K$, earning some premium $C$, and buy a put with the same strike $K$, ...
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### Intuitive explanation of put option pricing based on put-call parity

Assuming no dividends, the put-call parity equation says: $c + Ke^{-rT} = p + S$ where $c$ is the price of the European call, $p$ is the price of the European put, $S$ is the current stock price, $K$ ...
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### Under Put-Call Parity, why do we add the cost of carry to Call prices but subtract them from the Stock price and Put prices?

In Natenberg (1994) Chapter 11 he outlines the Put-Call parity relationships. ...
1 vote
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Why is the bid-ask spread of a in-the-forward/money American call (put) much larger than the out-of-the-forward/money American put (call)? I suppose the answer to the same corresponding question ...
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### Black-Scholes pricing of european call option

I am really confused on the usage of the greeks and the Black-Scholes model for option pricing. To gain some more understanding I am attempting to see if I can price a european call option under the ...
1 vote
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### How to prove Gamma is the same for a European call and European put with the same inputs?

I saw from a text "From put-call parity, call and put with the same inputs have the same gamma", but I don't see how put-call parity is related to Gamma. Can someone explain? Thanks!
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### Why is put-call parity defined differently by CME and Wikipedia?

In general, Wikipedia defines Put-Call parity as: C - P = D(F - K) ---------------- C = call price P = put price F = *FORWARD* price K = strike which can be re-...
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