> For the complete documentation index, see [llms.txt](https://finwhite.gitbook.io/quantolocalvol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://finwhite.gitbook.io/quantolocalvol/local-volatility-model-for-callable-quanto-option-valuation.md). # Local Volatility Model for Callable Quanto Option Valuation Local Volatility Model for Callable Quanto Option We review a model for computing the price, in the domestic currency, of European standard call and put options on an underlying foreign equity (stock or index) with tenor of up to 7 years. The function implements a local volatility based pricing method. The payoff in the domestic currency of a European option at maturity T is given by where The equity price process satisfies a risk-neutral stochastic differential equation (SDE) when where are no dividend payments. Let St denote the equity price at time t. We assume that the process satisfies a SDE of the form under the domestic risk-neutral probability measure: where We note that the volatility σ depends only on time and on the instantaneous value of the state variable S, but does not explicitly depend on W. The quanto-adjustment q is calculated by where Note that we also implement a second quanto-adjustment technique that is of the form where w\_k is a weight. Consider the calibration of the local volatility function based on market option prices or, equivalently, market Black’s implied volatilities. If there exists a smooth surface of either option price or implied volatility as a function of option strike and maturity, then this surface uniquely determines the local volatility function. Moreover, an explicit expressions for local volatility is provided. For example, if C denotes the price of a call option on a non-dividend paying stock, with a constant risk-free interest rate, then Local volatility model can also be applied to value callable exotic notes. Callable option is more volatile as callable events make the remaining part of the trade potentially be cancelled as a result of a trigger condition or an exercise option. You can find a good illustration on the topic of callable notes at In general, local volatility model is very useful tool for pricing equity derivatives. --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://finwhite.gitbook.io/quantolocalvol/local-volatility-model-for-callable-quanto-option-valuation.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.