# Questions tagged [black-scholes]

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

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### How does one transform the Black Scholes equation (u_t +0.5A^2 x^2 u_{tt} +Bxu_x - Cu= 0) to the heat equation [duplicate]

Given that A, B and C are constants, how does one transform (u_t +0.5A^2 x^2 u_{tt} +Bxu_x - Cu= 0) to the heat equation.
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### Correlated Wiener Process

I am in trouble with a task: I have a portfolio of 5 assets, and I Have the correlation among them, with a 5x5 matrix. Since each asset follows the BS formula: , I need to perform a montecarlo ...
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### No-arbitrage bounds on Implied Volatility under Black-Scholes

Suppose the overnight (1-day) at-the-money implied volatility is X% and the two week (14-day) at-the-money implied volatility is also X%. How would I go about finding the upper and lower no-arbitrage ...
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### How smooth is Black-Scholes?

For each variable $(S,T,K,r,q,\sigma)$ in the Black-Scholes formula, how many times can you take a partial derivative? Adjacently, is the nth order greek for some variable a constant? Thanks
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### Early Exercise of American Options on dividend-stock

I am reading the chapter 15 of Options, futures, and other derivatives by John Hull. Specifically, 15.12 Dividends-American Call Options. I am stuck while proving the fact that exercising an American ...
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### Formula for a Black-Scholes option [closed]

In a Black-Scholes market of two assets, we have the riskless asset $B_t = e^{rt}$ and the following stock: $$S_{t} = S_{0} \exp \left( \left( r - \frac{\sigma^2}{2} \right) + \sigma W_{t} \right)$$ ...
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### Black 76 and Asian Style Options on Shaped Power Futures

I am attempting to price a monthly lookback option on the gen-weighted average price of power at a particular solar plant over a given month. If the option settles at hub H, am I right to shape the ...
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### Black-Scholes - Security value with two sources of risk

Consider the Black-Scholes economy with two sources of risk. A security pays off $S_{1T} S_{2T}$ upon its maturity at time T, where $S_1$ is the level of the S&P500 index and $S_2$ is the price of ...
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### Solving the Black-Scholes for any arbitrary payoff

Good evening, I'm currently working on the following problem and I would like an opinion on it, Let's consider the Black-Scholes model with (time-varying) volatility, $\sigma = \sigma(t)$, and (time ...
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### Calculate error at all spatial indices for a given time step between BS equation and its numerical solution using explicit method

I am using the explicit finite backward difference scheme to discretize and calculate the price of an European call option in a discretization stencil. My goal is to find the error at a given time ...
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### Theoretical returns of Short Straddle in an efficient Options Market

Assumptions: Market is efficient All assumptions of BS Model apply Implied Volatility predicted using BS model is same as actual volatility in future. Needless to say that the volatility is constant ...
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### Replicate a claim in a complete market

Consider the Black-Scholes market wher $\sigma > 0$, and a claim paying $S_T^{\gamma}$ at time $T$, where $\gamma$ is some positive constant. How do I find the replicating portfolio of such a claim？...
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### Log Moneyness vs Log Strike

In How to calibrate a volatility surface using SVI, is said: "(log-moneyness would be more accurate) ". First, why do we talk about "moneyness", is it a reference of "being in ...
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### Sensitivities under Bachelier process

The sensitivity profile like (delta, vega, gamma etc.) of an option contract is quite established if the valuation model follow ...
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### What's the intuition behind there being a perfect linear relationship between option value and expected volatility?

I modelled option prices using the BS model at different levels of volatility. Surprisingly, I came out with a perfectly linear relationship. As volatility rises, so does the option value, which is ...
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### Hedge error - Willmot and Ahmad

I'm currently reading the paper: Willmot and Ahmad: Which free lunch would you like today, Sir? Delta Heding, volatility arbitrage. In case 1: They delta hedge with the actual volatility, by going ...
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