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Trinomial Option Pricing, Risk Neutrality, and Hedging

Article Quant Q&A · Author: G2MWF
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Summary

The document asks how to interpret risk neutral pricing in a trinomial option model. It observes that the model’s pricing formula depends on a parameter and wonders whether that parameter must be chosen to obtain a fair European option price. It also asks how pricing connects to hedging, given that backward induction in the binomial model supplies a replicating hedge as well as a price.

No answer or derivation is provided, so the document does not explain how to determine the parameter or construct a trinomial hedge. Its useful contribution is identifying the distinction a learner should investigate: a pricing formula alone does not show how the model’s assumptions support replication or risk neutral valuation. The note is limited to posing that conceptual question and offers no examples, evidence, or practical pricing guidance.

Key ideas

  • The note asks how a parameter in a trinomial pricing formula should be selected.
  • It distinguishes the question of option valuation from the construction of a hedge.
  • It contrasts trinomial pricing with binomial backward induction and replication.
  • The document leaves the parameter choice and hedging connection unresolved.

Tags

OptionsDerivatives pricing
Full text
# Trinomial model option pricing


# Trinomial model option pricing












If I have well understood, in the trinomial model we have a kind of risk neutral pricing formula that depends on a parameter. This means thaht as in the binomial model, we could use directly this formula to obtain the price of an option (European type) if there was not this dependency on a parameter. So the problem is to find the value of the parameter that gives a "fair price" ? However, in all I have mentioned, we do not talk about the hedging, so what link can be made with the hedging if there is one ?

In the binomial, it is clear since we can find by backward induction the perfect hedging and thus the price.

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