# Questions tagged [black-scholes]

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

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### Volatility estimation based on a 60 days range

In Hutchinson et al: A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Network (1994) paper (link), to estimate $\sigma$ for the Black-Scholes formula, it says (p. 881)...
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### Stocks with same volatility but different drifts

In the book Quant Job Interview Questions & Answers, in section 2, question 2.4 says suppose two assets in a Black-Scholes world have the same volatility but different drifts. How will the price ...
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### Asian option sensitivity

I am looking for some materials for profiling all options sensitivities for Asian options with both geometric averaging and arithmetic averaging . The underlying price $S_t$ follows a standard GBM. Is ...
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### How to calculate dividend yield - option pricing

Hey how do you calculate the dividend rate if you want to price your stock options eg apple? Just take the dividends paid last year and divide by today's share price? This page reports 0.85% (https://...
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### Over-night Black-Scholes

I have a question for Black-Scholes. It is a continuous approach, but the real market closes every day. So for the Black-Scholes, how do we count the time effect of during the time when the market is ...
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### Can a down-and-out barrier call option be priced using the Black & Scholes formula or should it be approximated?

I am trying to price of a Down-and-Out Barrier call option with leverage. When the price of the underlying asset hits a certain barrier (B), the option becomes worthless. The issuer of these options ...
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### Black Scholes model calibration

the only parameter in the Black Scholes model that needs to be estimated is the volatility. Which approach is correct: Estimation of volatility from daily log returns Estimating volatility by ...
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### Market price of risk on two assets

Under the assumptions of the Black--Scholes model, I read that the market price of risk of two assets $S_1$ and $S_2$ are the same, if they both follow Geometric Brownian motion driven by the same ...
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### Can “Turbo warrants” be priced using the Black & Scholes model?

I am trying to model the pricing of an asset called a "Turbo warrant", which to me looks a lot like a Down-and-Out Barrier option with leverage. When the price of the underlying asset hits a ...
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### I just got Matlab, what are some options that I should model in a jump diffusion

Don't worry I understand mathematics: ito's calc, martingales, etc. I am just curious what options I should test, and from what indices. Is there stuff I can test from the 2008 crash to measure their ...
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### Are there stocks dynamic that cannot be represented by Generalized Black Scholes model?

The generalized Black Scholes Model refers to a stock dynamic that satisfy $$dS(t)=S(t)(\mu_t dt+ \sigma_t dW(t))$$ By martingale representation theorem, it seems that if there is a risk neutral ...
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### Why are these deep in-the-money FLEX options seemingly bought at a discount?

98% of the initial reference value is .98 x 267.88 dollars, which equals 262.52 dollars. However, the market value of each call contract they purchase is 247.42 dollars. How are they purchasing these ...
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### Operator splitting method on three assets black scholes equation

Currently I am studying finite difference method on derivatives with three (or more) underlyings and little bit confused on operator splitting method because two papers have different result. For the ...
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### How to understand broken wing butterfly option strategies?

I feel very confused about the greeks analysis for the broken wing butterfly strategy. Let's say for the stock ABC, we enter into a such strategy: we long a put option with strike $k_1$ and another ...
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### What is the meaning that Geometric Brownian motion is leptokurtic? [closed]

Does this have any relation to the symmetry of the normal distribution?
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### Realizing profit with Gamma Trading doubt

Lets suppose we have a delta-neutral portfolio and that we want to trade the gamma. If we are long gamma, we can profit from every rebalancing to keep the portfolio delta-neutral. Lets suppose the ...
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### Black-Scholes Implied Volatility

I'm working my way through the following paper: Malz. A. M. (2014). A Simple and Reliable Way to Compute Option-Based Risk-Neutral Distributions I am completely stuck on the following derivation. The ...
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### Higher moments of a straddle

Following the logic of Ben-Meir and Schiff (2012) and this question the first, second, third and fourth raw moments of a put are: Similarity, for a call it is as follows: where and ...
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### What are some alternatives to Geometric Brownian motion that can be used in the Black-Scholes? [closed]

I hear that there are many extensions to the black scholes model to make it more realistic, however, GBM does not account for volatile swings. Is there any sort of alternative approach to use instead?
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### Implicit finite difference method always guarantees positive and stable price of derivative?

For the following black scholes pde $$f_t + rSf_S+\frac{1}{2}\sigma^2S^2f_{SS} = rf$$ By denoting $f_{i}^{n} =$ Price of derivative at price node $i$ and time node $n$ and assume uniform grid, the ...
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Compute the price of a derivative which has pays $\log(S_T)S_T$, you can assume that the Black Scholes model is valid. Using the stock measure we can write the expectation as D(0) = S_0 \mathbb{E}... 4answers 192 views ### Price of Call Option with or without jumps Suppose two assets in the Black Scholes world have the same volatility, but different drifts and that one has downward jumps at random times. How does this affect the option prices? I would have ... 1answer 200 views ### Historical volatility - Black Scholes How do you best incorporate the weekends in the calculation of the Black Scholes historical volatility? (Of course historical volatility serves as approximation, if the market price of the options is ... 1answer 158 views ### Gamma PnL from Itô's Lemma derivation The change in a call portfolio (f), derived from Itô's Lemma, is: \begin{align*} \left( \frac{\partial f}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2 f}{\partial S^2}\right)\mathrm{d}t &=... 0answers 48 views ### Can option chain data be used as a quick and dirty substitute for proper pricing calculations for non-traded options? I wonder if the option chain data that is published everyday by websites like Yahoo finance can be used to quickly price options that are not yet traded? So in other words, to estimate option prices ... 0answers 42 views ### Convenience yield I need to price an option on gold in some local currency. If I use the Black Scholes formula, then I need to input convenience yield for spot gold. Given generally available market data, how can I ... 1answer 130 views ### How to best predict option prices using Brownian motion and compare it to the Black and Scholes model? I am trying to use Brownian motion to predict option prices and compare the outcomes to Black and Scholes. For this purpose, I would like to calculate the average returns (mu) and volatility (sigma) ... 1answer 94 views ### VBA Black Scholes Implied Volatility I keep getting a Implied Vol. = to my initial guess, My code is as bellow ... 1answer 63 views ### Kurtosis of a straddle I want to determine the kurtosis of a straddle. My question is closely related with the following topic here. According to the following paper of Ben-Meir and Schiff (2012) the expected value of a ... 0answers 51 views ### Different distributions for option pricing So the classic BS assumption of lognormal prices imply that the stock price can not be negative. Now since recently also oil prices were negative I was wondering, whether it would be possible to ... 0answers 47 views ### R: How do i finish the tails in the risk neutral density, obtained from option prices Im currently working on constructing the risk neutral probability distribution of a stock, based on the option prices. In doing so, i calculate the implied volatilities from the option prices, and ... 3answers 57 views ### Implied Volatility, annualized quantity ? And Total Implied volatility so Implied Volatility is computed by equalizing the value of the call option given by the black and scholes model with the one observed. Then, by inversing C_{BS}, one gets "\sigma_{IMP}"... 2answers 97 views ### May someone please explain the intuition behind the Black-Scholes Equation? Consider the Black-Scholes equation for a European Call Option, \begin{equation} \begin{cases}\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r\frac{\... 1answer 56 views ### FX Call under stochastic rates and deterministic volatility Lets denote S_t, r^d_t,r^f_t respectively the FX spot, the domestic rate and the foreign rate at time t. Lets \mathbb{Q}^d , \mathbb{Q}^f respectively be the domestic and foreign mesures,... 2answers 74 views ### Binary Option Valuation With Skew In searching for methods of valuation of Binary options with skew, I have found two formulas which are at odds. I cannot find any other references to this valuation formula. Should Vega be positive ... 1answer 55 views ### Black & Scholes formula derivation from a Binomial Tree - John C. Hull I am reading "Option, Futures and other Derivatives" by John C. Hull, and on Appendix chapter 13, he derives BSM formula from a Binomial Tree. When he builds U2, I just don't understood how to get ... 2answers 69 views ### How are option values in real life calculated without volatility? Implied volatility is the volatility that when inputted in the Black-Scholes model, it returns the theoretical market price of a European option value. I understand that implied volatility is not ... 2answers 87 views ### Calculating the 0.50 delta strike According to most books the ATM option is the option with a delta of 0.50. However, this is only the case when the distribution is normal. The more positively skewed the distribution, the further the ... 2answers 66 views ### About the log return in the Black&Scholes model I'm currently studying the Black&Scholes model and I'm not sure about the following thing: the log return, say r, doesn't evolve in time? I mean, dr/dt = 0, its derivative is zero? Does only its ... 1answer 69 views ### Does Black Scholes + Stochastic interest rates result in a unique price Black-Scholes with its assumptions results in a unique price for the call. If we introduce stochastic interest rates, would this still remain the case? 2answers 61 views ### Stochastic Volatility Models - are they complete markets? I'm reading about stochastic volatility models - the ones which resulted after Wiggins proposed in 1986/7 that \sigma in Black-Scholes should be a stochastic process rather than a constant. In ... 1answer 50 views ### Is the forward price equal to the future price? If f^{T_1}(t) is the price of a forward and F^{T_1}(t) is the price of a future on some stock, both maturing at date T_1 and with the assumptions: no dividend constant interest rates no ... 0answers 125 views ### Black-Scholes market and payoff with integrals I am struggling with the following exercise: Prove that on Black-Scholes market, with some parameters r, \mu, \sigma >0, a payoffX=\int_{0}^{T}\ln \frac{S_t}{S_0}\mathrm{d}t+\frac{1}{\sigma}\...
I would like to prove that if there exists $(X_1,\ldots,X_n)$ satisfying $\mathbb E[\int |X(s)|^2 d[Y]_s]<\infty$ (for a standard filtered probability space $(\Omega, F,( F_t)_{t\ge 0},\mathbb P)$ ...