Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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How to calculate sigma in order to calculate delta? [closed]

I am calculating option delta using py_vollib.black_scholes ...
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Longstaff & Schwartz algorithm - Python: American option cheaper than European option

I have implemented the Longstaff & Schwartz algorithm for pricing American Option in Python, but I ran into an issue while doing some experiments: sometimes, for the same option, I get a higher ...
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Future Implied Price from Option Implied Distribution

Been reading on option implied distributions and understand that this can be transformed into a confidence interval/fan chart showing the implied future price. Was wondering how I could go about doing ...
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How to and What is the price of an American call option for non-dividend stock?

I want to know how to price an American call option for non-dividend stock (with concrete and simple binomial pricing model, with risk neutral assumption). I understand that for an European call ...
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Option pricing boundary condition

I am currently working on this paper "https://arxiv.org/abs/2305.02523" about travel time options and I am stuck at Theorem 14 page 20. The proof is similar to Theorem 7.5.1, "...
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Pricing PDE of Asian option by Shreve

I am currently working on "Stochastic Calculus for finance II, continuous time model" from Shreve. In chapter 7.5 Theo 7.5.1 he derives a pricing PDE with boundary conditions for an Asian ...
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1 vote
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Implied Distributions from forward prices

I understand that the common way to arrive at an implied distribution for an underlying is through the price of its call options as per the Breeden-Litzenberger formula. I am wondering if its possible ...
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Computing Derivative Security with Change of Numeraire

Under Black-Scholes, price a contract worth $S_T^{2}log(S_T)$ at expiration. This is a question from Joshi's Quant Book (an extension question). Ok, so I solved this with 3 different methods to make ...
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Deep vs "shallow" calibration of option pricing models

I am currently investigating the application of deep learning in calibrating option pricing models, specifically, models of rough volatility, such as rBergomi. While there is a lot of research on ...
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Breaking down gamma PnL by time

Let's say in one day time, underlying price S goes up by $2.4. Then the gamma PnL should be$\frac{1}{2}\gamma_0 (2.4)^2$. Let's assume that in every hour the underlying goes up by$0.1. Then how do ...
194 views

How does the interest rate affect the implied volatility of options, especially ITM?

What would be a good reference to understand how the interest rate (r) or dividend yield (q), and I guess the differential between the two, affect the implied volatility of the options? If I look at a ...
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What accounts for the difference between these two option strategies?

Same underlying, same strike, same expiration. One is a covered call, the other is cash secured put. These are screenshots taken from a website. As you can see, they are similar, but the max win ...
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Thinking about time value of an option

In addition to Wikipedia, YouTube and other internet sources, I'm reading Timothy Crack's "Basic Black-Scholes: Option pricing and trading". Most of these sources suggest that it is fairly ...
1 vote
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General Binomial Method for option pricing

I am reading the book "Principles of Corporate Finance" 12th edition by Brealey, Myers and Allen. In the 21st chapter on Option pricing, they discussed the General binomial method for option ...
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Different notations for times variable in Haug's book

I am reading the book by Haug, 2007 on the pages 186-188 one can find the Turnbull and Wakeman approximation for arithmetic avarage rate option. The approximation adjusts the mean and variance so ...
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1k views

Bloomberg terminal option data calculation

EDIT based on the answer provided, I have followed, but still I cant match the bbg data with my calculations, could some advise how to match the bloomberg Price given the data? ...
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Derivation in Jaeckel's "By Implication" paper

In this paper by Jaeckel (2006), he derives the asymptotics for the option price $b$ as: \begin{align*} \lim_{\sigma \to \infty}b= e^{\theta x/2} - \frac{4}{\sigma}\cdot \phi(\sigma/2) \tag{2.7}\\ \...
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Validating an option-implied risk-neutral distribution by integrating it twice and comparing the resulting "prices" with the original ones

From Breeden-Litzenberger, we know that the second derivative of a European call option's price with respect to the strike price is equal to the risk-neutral probability density function of the ...
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1 vote
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Finite difference methods for an Asian call with boundary conditions

I have a question please. I have to find the price of a Asian call using a finite diffenrece method. Here the article, if u want to look it up, it's page 2-4: "https://www.researchgate.net/...
172 views

How to calibrate a volatility surface using SSVI with market data?

Context I'm a beginner quant and I'm trying to calibrate an vol surface using SPX Implied Vol data. The model is from Jim Gatheral and Antoine Jacquier's paper https://www.tandfonline.com/doi/full/10....
259 views

Verifying my understanding of replicating portfolio, hedging and option pricing

Under risk neutral measure, we use replicating portfolio to mimic the value of derivative (for example European options). Many literatures use the word "hedging" to describe the replicating ...
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Kou model — solving PIDE for European and American options in Python

Toivanen proposed$^\color{magenta}{\star}$ a method to solve the partial integro-differential equation (PIDE) with a numerical scheme based on Crank-Nicolson. In particular, he proposed an algorithm ...
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Kou model - can't reproduce prices of European Option from Toivanen and Forsyth [duplicate]

I have implemented the Kou option model for pricing vanilla option. I have checked that my program can replicate the price of the option in the original paper of 2002. However, when I use it to price ...
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What will be the payoff equation of a GBPUSD European Exotic option/FX forward with Notional in USD [duplicate]

Given the currency pair , GBPUSD with spot price as $S_t$ at time $t$, Strike price as $K$, $I$ is an indicator function indicating if GBPUSD is below the "Knock-in-Rate" at expiry, $L$ ...
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Price a contingent claim with payoff $(S_{1T}-S_{2T})^+$ at time $T$

Two stocks are modelled as follows: $$dS_{1t}=S_{1t}(\mu_1dt+\sigma_{11}dW_{1t}+\sigma_{12}dW_{2t})$$ $$dS_{2t}=S_{2t}(\mu_2dt+\sigma_{21}dW_{1t}+\sigma_{22}dW_{2t})$$ with $dW_{1t}dW_{2t}=\rho dt$....
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what is the point of SABR model as an interpolation tool if we can already observe the whole vol cube from the market

on BBG and other data providers, it is common that you can find the whole vol surface/cubes. What is the point of the SABR model as an interpolation tool? why cannot people just linear interpolate the ...
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