# Questions tagged [black-scholes]

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

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### Derivatives without analytic expressions?

I was wondering if there exist options or other derivatives that do not have a known closed-form analytic expression (i.e., some sort of Black-Scholes PDE) and are usually priced using Monte Carlo ...
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### Option time value is Nd1-Nd2

I can't find the below statement anywhere (rearrangement of Black-Scholes formula) : $C(0, S) = e^{-rT}N_2[F-K] + [N_1-N_2]S$ $F$ being the forward, it reads as a straightforward decomposition to ...
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### Implied Volatility Surface Interpolation for fixed moneyness and maturity on each day of the calendar

I'm new to quantitative finance and interested in performing a PCA on the implied volatility surface. However, my dataset displays certain point changes over time. As a result, I need to interpolate ...
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### Effect of number of monitoring points on Asian Option Price

I want to understand conceptually the expected effect of the number of monitoring points used during the average calculation on Asian options pricing and the reason of such effect. Asian Options ...
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### How to use GARCH/ARCH/EGARCH volatility forecasts to compare the Black Scholes constant volatility assumption with GARCH/ARCH/EGARCH volatility

I should preface this by saying I am an undergraduate physics student, this is more of a side interest to me, so I apologise if I am missing something obvious. I am not following a formal class or ...
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### Problem matching prices of Black-Scholes vs. GARCH(1,1) in Duan (1995)

In the paper of Duan (1995) the author compare European call option prices using Black-Scholes model vs. GARCH(1,1)-M model (GARCH-in-mean). To be brief, the author fits the following GARCH(1,1)-M ...
1 vote
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### Is there anyway to compute the CEV-implied volatility from option prices?

Under Black-Scholes, there exists a solution for the option price for a volatility. The volatility can then be backed out from the option price using numeric methods. For the constant-elasticity of ...
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### Exact delta-hedging for endogenous payoffs

I would like to derive the exact delta-hedging strategy in the Black-Scholes market to replicate the following non-standard endogenous payoff. The particularity is that the payoff does not only depend ...
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### Binomial tree convergence tree towards BS equation - Struggle with a limit

I am trying to prove that the Binomial tree pricing method converges towards the Black and Scholes model, but I am struggling on a specific step. I don't understand how the limit of p*(1-p) is ...
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### Solve for spot price given delta [closed]

I can use Black Scholes or Bjerksund Stensland to solve for delta given spot price, strike, expiration, vol, interest rate, etc. But is there a direct solution to solve for spot price given delta, ...
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### Does skew flatten with a decline in volatility?

In Trading Volatility by Bennett, he says: If there is a sudden decline in equity markets, it is reasonable to assume realised volatility will jump to a level in line with the peak of realised ...
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### Find strike of an option based on a delta without option price

I would like to use the Black Scholes model to get the strike based on delta, without having the option price. So I read this: From Delta to moneyness or strike Which show that we can get a strike ...
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### Access expired options data [duplicate]

I would like to access expired options data, for example, I would like to know the evolution of the call price for a certain option, during the month before the expiry date, which would for example be ...
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### Derivation of Call Theta from Black Scholes Model [closed]

How is call theta mathematically derived from Black Scholes Model (without approximation) ? Please help me understand each step mathematically.
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### First known reference using martingale theory to derive BS formula

What is the first known paper which derives the Black-Scholes valuation formula for an option (1973) using martingale machinery - instead of PDEs?
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### Delta of a forward ATM option

Reading: What are some useful approximations to the Black-Scholes formula? I understand that a ATM Call option can be approximated to $$C(S,t)≈0.4Se^{−r(T−t)}σ \sqrt{T−t}$$ Also, I often hear that an ...
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### University problem about Bond option [closed]

Good morning, Next week I'll have Derivates Final test and I've a doubt about Bond Option. If I have one ZCB, price 90 with 3 month maturity and strike 100, and I want a minimum yield of 2%, what type ...
1 vote
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### What happens trying to price derivatives starting from a non-geometric brownian motion?

To get a better understanding, I tried going through BSM-model starting from a non-geometric brownian motion. However, during the derivation I got stuck, which led me to a specific question. The set-...
1 vote
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I was trying to understand why the Black and Scholes PDE for the value of an option, $V (F , t)$, with the forward price, $F$, as underlying is $$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2F^2\... 0 votes 0 answers 104 views ### University Problem about interpolation Implied volatility BS Model (volatility smile) Good morning, this is my first question on this forum, I'm writing from Milan (Italy) and I have a question about a University Problem. The problem is about entering in a Long Range Forward (buy a ... 1 vote 0 answers 64 views ### Finite Difference Application We all know that the traditional BS equation is:$$\frac{\partial \mathrm V}{ \partial \mathrm t } + \frac{1}{2}\sigma^{2} \mathrm S^{2} \frac{\partial^{2} \mathrm V}{\partial \mathrm S^2} + \...
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BSM gives the following formula for option gamma $$\Gamma = \frac{e^{-qT-\frac{d_1^2}{2}}}{S\sigma\sqrt{2\pi T}}$$ where $$d_1=\frac{\ln\frac{S}{K}+(r-q+\frac{1}{2}\sigma^2)T}{\sigma\sqrt{T}}$$ ...