No-Arbitrage Pricing of Options on Options

Summary

The document raises the question of how to price a European call whose underlying is itself the value of another European call. It defines the inner option by its underlying asset, strike, and expiry, then asks for a no-arbitrage price for an outer call on that option value with its own strike and expiry.

This is a conceptual prompt rather than a worked explanation: it provides no model assumptions, replication argument, pricing formula, examples, or discussion of practical uses. A complete valuation would need to specify the underlying dynamics and how the inner option’s value evolves before the outer option expires. The excerpt therefore identifies a derivative-pricing problem but supplies no evidence or method for resolving it.

Key ideas

• An option can be written on the market value of another option.
• Pricing the outer option requires modeling how the inner option value changes over time.
• The prompt does not specify dynamics, replication assumptions, or a valuation method.
• No formula, example, or practical assessment is provided.

Tags

# Derivatives of derivatives


# Derivatives of derivatives












Has financial derivatives of financial derivatives ever been considered in academic or practical settings? Is it useless/useful?

Say $C(S_t;K,T)$ is a European call on an underlying $S_t$ with strike $K$ and expiry $T$. Then what is the no-arbitrage price of a European call on the above call, $C^*(C(S_t;K,T);K^*,T^*)$ and questions like these?

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