Max of Put

Quantitative Finance Level 1

The stock is currently trading at $30. What is the maximum price of the Put on the $20 strike, expiring in 1 year?

No maximum price exists $10 $30 $20 $50

1 solution

Chew-Seong Cheong
Apr 22, 2015

The price of an option cannot be so high that arbitrage opportunity exists. Arbitrage opportunity exists when a call price is higher than the underlying price and a put price is higher than the strike price. Therefore, the maximum price for a call option is the price of the stock. The maximum price for a put option is the strike price, which is $\boxed{\$20}$ in this problem.

Can you describe what the arbitrage opportunity is?

Calvin Lin Staff - 6 years, 1 month ago

I don't totally agree with you.You are right about the put price;however call price can be a lot higher than the actual stock price depending on the volatility and exercise date.

Sinan Ulusoy - 5 years, 6 months ago

That's not true. The Call price is indeed capped by the stock price, and it's independent of the volatility and exercise date. If the call price was greater than the stock (ask) price, then we have a pure arbitrage opportunity, by selling the call for $S + \epsilon$ and buying the stock for $S$ , and then holding this position to expiration.
- If the call is exercised, we deliver the stock that we bought, and pocket the difference $\epsilon$ .
- If the call is not exercised, we sell the stock for $T$ , and pocket $T + \epsilon$ .

Hence, the call price cannot be higher than the stock price.

Phrased in terms of Put Call Parity , if the put is worth at most $X$ the strike price, then since $C - P = S - X \Rightarrow C = S - X + P \leq S - X + X = S$ , this also shows that the call price is at most the stock price.

Calvin Lin Staff - 5 years, 6 months ago

Max of Put

1 solution

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