Option Pricing Without Greeks or Risk-Free Reinvestment

Summary

The document poses an interview-style question about quoting a European call on an equity priced at 100, with a strike of 150. It asks what minimum premium would guarantee no losses when the trader has no Greek information, cannot earn the risk-free rate on cash, and can hedge only through the spot market.

No pricing method, answer, or supporting evidence is provided. The question highlights that a guaranteed-loss-free quote depends on assumptions about the underlying price path, volatility, hedging costs, and the trader’s ability to manage exposure. With those details unspecified, the document does not establish a unique minimum price. It is best read as a prompt about the limits of option pricing and hedging under incomplete information, rather than as a worked strategy.

Key ideas

• The document asks for a minimum quote on a European call when the underlying is below the strike.
• It restricts hedging to the spot market and excludes risk-free cash reinvestment.
• It provides no solution or assumptions sufficient to derive a guaranteed minimum premium.

Tags

# What is the minimum price of an option, given no information about Greeks?


# What is the minimum price of an option, given no information about Greeks?












I was asked this interview questions for an analyst level structuring role and it has been bothering me since I can't figure it out:

Assuming the price of an equity is 100, what is the minimum price to quote a 150 strike European call option to guarantee you make no losses?

- You have not information about Greeks;

- You cannot reinvest cash at the risk free rate;

- You only have access to hedging in the spot market.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.