# Questions tagged [black-scholes]

Black-Scholes is a mathematical model used for pricing options.

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### How to conduct Monte Carlo simulations to test validity of Black Scholes for a specific option?

In reference to the original Black Scholes model, what approach is best to test the model in a rigorous way? Is there a standard approach that can accomplish this in a reasonable amount of time? ...
747 views

### What are the main differences in Jump Volatility and Local Volatility

Is a JV model simply Local Vol + Jump Diffusion? If so, it seems logical that an existing JV model be able to be used for valuation of both Vanilla and Exotic options. Is this true? Does a Local ...
• 497
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### What tools are used to numerically solve differential equations in Quantitative Finance?

There are a lot of Quantitative Finance models (e.g. Black-Scholes) which are formulated in terms of partial differential equations. What is a standard approach in Quantitative Finance to solve these ...
• 509
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### Can the Heston model be shown to reduce to the original Black Scholes model if appropriate parameters are chosen?

Summary For Heston model parameters that render the variance process constant, the solution should revert to plain Black-Scholes. Closed from solutions to the Heston model don't seem to do this, even ...
• 343
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### Black--Scholes hedging argument

I'm trying to understand the standard hedging argument to derive the Black--Scholes PDE. There's one aspect of the derivation which I can't get passed and I'd be very grateful for some clarification ...
• 111
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### What is a self-financing and replicating portfolio?

I try to understand the derivation of the Black-Scholes equation based on the "constructing a replicating portfolio". From mathematical point of view it looks simple. We assume that: Stock prices is ...
• 509
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### What are the main limitations of Black Scholes?

Pls explain and discuss these limitations, and explain which models can I use to overcome these limitations. Alternatively, provide examples of how to modify the original Black Scholes to overcome ...
457 views

### Appropriate measure of Volatility for economic returns from an asset?

In order to use Real Option Valuation (ROV), using Black-Scholes equation, I must know the volatility of the economic returns for T years. Knowing this information what could be the appropriate ...
5k views

### Black-Scholes formula with deterministic discrete dividend (Musiela approach)

For deterministic discrete dividend, there are two approach Musiela approach, works when every dividend are paid at maturity of the option. Hull approach, works when every dividend are paid ...
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### Is it possible to demonstrate that one pricing model is better than another?

Take the classic GBM (geometric Brownian motion) model for equities as an example: ds = mu * S * dt + sigma * S * dW. It is the basis for the classic Black-...
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