Replicating a Power Payoff in the Black–Scholes Market

Summary

The document poses a derivatives-pricing question: how to construct a replicating portfolio in a Black–Scholes market for a claim that pays a positive power of the stock price at maturity. It specifies positive volatility and a payoff of the form stock price to the power γ, but provides no derivation or proposed portfolio.

The topic points toward finding a self-financing hedge whose value matches the claim’s payoff at maturity, using the stock and risk-free asset in the Black–Scholes framework. The document gives no calculations, evidence, or discussion of the conditions under which replication holds, so it cannot establish a particular solution. Readers would need additional material to derive the portfolio and examine how it depends on the exponent, volatility, and time remaining.

Key ideas

• The claim pays a power of the underlying stock price at maturity.
• The question assumes a Black–Scholes market with positive volatility.
• The document asks how to construct a replicating portfolio but provides no answer or derivation.

Tags

# Replicate a claim in a complete market


# Replicate a claim in a complete market












Consider the Black-Scholes market wher $\sigma > 0$, and a claim paying $S_T^{\gamma}$ at time $T$, where $\gamma$ is some positive constant. How do I find the replicating portfolio of such a claim？

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