# Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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### Change in Option Price given Change in Implied Volatliity, Moneyness, and Maturity

I have an implied volatility surface parametrized into moneyless-maturity coordinates. At each period of time, I only have access to an option's moneyness (K/S), maturity, and change in implied ...
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### Target Realized Volatility or Realized Variance in Forecasting

There are many academic paper doing volatility forecasts using realised variance and realised volatility interchangeably -- both targeting the proxy estimation of sum of squared returns (realized ...
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### resolve the DUPIRE Forward PDE

I want to implement the "Dupire forward PDE". I will use this PDE to calibrate a parametric local volatility model. Could you recommend an article or link that explains concretely how I can ...
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### Simple arbitrage pricing of bond option

This is Tuckman fixed income security textbook. The text here is trying to price a 990 six month call on a six month zero bond. When we replicate the portfolio, where is the F_.5 coming from? My ...
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### Vol Shift by Term over Time

Below is a plot of AAPL vol vs. Strike for October and November, last market close vs 3 weeks prior. The plot shows that both curves shifted up by an approximately constant amount with the October ...
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### Potential arbitrage opportunity or fallacy?

Suppose we have two European options with the same expiration: a call priced at $c$ with strike price $K_1$ and a put priced at $p$ with $K_2 (>K_1)$. Further, suppose the zero-points of the two ...
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### Volatility in simulated paths different to monte carlo parameters

I am trying to convince myself that I have set up my monte carlo simulation correctly by looking at the results and trying to get them to agree with the model parameters. Please help me understand ...
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### FX risk reversal approximation

i see this risk reversal approximation in Uwe Wystup's https://www.mathfinance.com/wp-content/uploads/2020/09/wystup_vannavolga_eqf.pdf in which the approximation of a risk reversal is given by: vega ...
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### What pricing curve to use for different instruments? [duplicate]

When pricing derivatives, their price depends on some yield curve, which is used to discount future cash flows. But there are many yield curves, dependent on what they're bootstrapped from. There's ...
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### Price of options when exercise date doesn't match nodes of BDT Tree

I think I'm missing something obvious here, but here I go. I'm studying pricing of bonds with embedded options using Black Derman Toy. I understand tree construction and its application for simple ...
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1 vote
In chapter 2 of Bergomi's book on stochastic volatility, we have dupire's formula given as \sigma(S, t)^2 = \left|\frac{\frac{\partial C}{\partial T} + (r-q)K\frac{\partial C}{\partial K} + qC}{\...