Computing Theta for a Down-and-Out Barrier Put

Summary

The document asks how to calculate theta for a down-and-out barrier put. It presents a decomposition of the barrier option into vanilla put and digital put terms evaluated at the current asset price and at a reflected price involving the barrier. The barrier level and the asset price enter several terms, so differentiating the full expression requires attention to how each component changes with time.

The author reports applying standard theta formulas to the vanilla and digital options but obtaining a result that differs from an expected answer. The text asks whether this approach is correct and requests a method for finding the barrier option’s theta. It provides no answer, numerical example, model assumptions, or specification of the expected result. Consequently, it identifies a practical derivatives-pricing problem and a proposed pricing representation, but does not establish the correct differentiation procedure or discuss complications such as barrier conventions and monitoring assumptions.

Key ideas

• The question concerns theta for a down-and-out put option.
• A proposed representation expresses the barrier put through vanilla and digital put components.
• The expression uses both the asset price and a reflected price determined by the barrier.
• Applying component option theta formulas did not produce the expected result for the author.
• The document does not provide a derivation or specify the assumptions needed to compute theta.

Tags

# Greeks(theta) of a Down-and-Out barrier option


# Greeks(theta) of a Down-and-Out barrier option












I am trying to figure out the theta for a down-and-out barrier put option. After some research of my own, I found out that a down-and-out put can be expressed as $$ P_V(S_0, S_0)-P_V(S_0, H)-(S_0 - H)P_D(S_0, H) - \frac{H}{S_0}(P_V(\frac{H^2}{S_0}, S_0) - P_V(\frac{H^2}{S_0}, H) + (S_0 - H)P_D(\frac{H^2}{S_0}, H)) $$ where $P_V$ is a vanilla put and $P_D$ is a digital put and $H$ is the barrier.

Using this formulation, I used the usual greek formluas for the vanilla and digital options. However, I am not getting the result that I am supposed to.

This made me suspicious about my approach, and I wanted to check whether my approach was correct. If it is incorrect, I would very much appreciate if someone could tell me how to find the greeks (theta) of a barrier options, down-and-out put in particular.

Thank you in advance.

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