# Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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### Binomial Model Is Leading to More Expensive Options as Number of Periods Grow

I've coded up a binomial model. It spits out the right numbers that the book I'm currently reading is using for the given inputs. For example, Stock Price 100 Strike Price 100 Number Of Periods 3 ...
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### Making portfolio Delta and Gamma neutral using 2 derivatives

We have an option portfolio with delta =2 and gamma 3 and we want to making this portfolio delta and gamma neutral using two derivatives D1 and D2: ...
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### Historical volatility calculation to price options with the Black-Scholes formula

I'm looking for a reference algorithm for calculating historical volatility to price options. I know there are several volatility calculation models that use the time series of the underlying's ...
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### Are there volatility models dependent on returns?

When I look at the relationship between volatility and price, I see a clear negative correlation as shown in this figure (SPY and VIX prices today looking back 1 year). The common volatility models (...
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### Do daily returns from a distribution with skew and/or kurtosis lead to options implied volatility skew?

I've been trying to price a call option using a Monte Carlo approach with the specific goal of showing implied volatility skew. I'm using the sinh-arcsinh transformation to make the random numbers I ...
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### What's the point of having an accurate option pricing model?

Just curious what's the actual reason of having an accurate option pricing model? For e.g. an option pricing model fits the volatility surface incredibly well, then what? Do practitioners actually use ...
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### Formula for the discounted payoff of a digital option

In "Heard on the Street" it states that the expected discounted payoff of a digital option is $$H\exp^{-r(T-t)}N(d_2)$$ where $H$ is the payoff of the option, the exponential is the discounting. ...
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### Differences in bull put spread option strategy

I am supposed to construct a profit and loss diagram for a bullish spread strategy: −1put($X_{1}$) + 1put($X_{2}$) and compare it to the profit and loss diagram for the strategy: −10put ($X_{1}$)+ ...
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### Where could I get European non-dividend option data

I am pretty new to option pricing. I got a task asking me to price a stock option, which should be an European non-dividend option, and compare my price to its quote. I used to use TSLA data ...
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### Nonlinear Black-Scholes model Vs linear Black-Scholes

I am working on a project related to Nonlinear BS partial differential equation, with terms for transaction costs and/or discrete hedging. I have two questions: Is there any exact solution to the ...
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### Mark Joshi uses forward price to price an option that pays $S_t^2-K$ if $S_t^2>K$ and zero otherwise? Why can we do that?

The following question is taken from Mark Joshi's Concepts and Practice of Mathematical Finance, second edition, Exercise $6.6$ Suppose a stock follows geometric Brownian motion in a Black-Scholes ...
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### In Carr-Madans option pricing method, why do they use FFT?

In the famous fourier option pricing method by Carr-Madan, (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.348.4044&rep=rep1&type=pdf), the crucial formula is They evaluate this by ...
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### Show that $Ae^{rt}$ is a solution of the Black-Scholes equation. Why should this be so?

The following is taken from Mark Joshi's Concepts and Practice of Mathematical Finance, second edition, exercise $5.6$. Question: Show that $Ae^{rt}$ is a solution of the Black-Scholes equation. ...
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### Option Bounds in a risk-averse incomplete market

I was reading the article "On option pricing bounds" by Ritchken(1985). It uses linear programming to determine options upper and lower bounds. Given a single period model, the stock price will have ...
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### Why does the price of a butterfly spread increase are rate exponential [closed]

I know that stock prices are assumed to be Stochastic processes that follow Geometric brownian motion. The expectation of stock prices at time T given stock price at time 0 is: $e^{-rT}S_0$. However, ...
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### Replicating portfolio with stock, bond and call option

I am trying to interpret: I am having trouble interpreting the replicating strategy: Context: $\phi$ is a generic payoff function, 0 < S < $\infty$, assumed throughout to be twice ...
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### Alternative derivation of Black Scholes by Merton

I am currently reading the Theory of Rational Option Pricing (1973) by Robert Merton. In the paper, I encountered a section under the title "An Alternative Derivation of the Black- Scholes Model". I ...
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### Reading this ichimoku cloud how do you read this wdfc chart?

Having trouble reading the charts as the breakouts aren’t clear What do you see in this chart?
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### Quesion about the VBA function of continuous cap look up [closed]

Here is the VBA function to calculate the cap price Can anyone tell me what is N and t0? From the textbook, N = the number of reset (or payment) dates and t0 = time until the first reset date. But ...
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### Pricing Equity Swaptions

Consider a swaption to enter into a standard equity swap as a fixed-rate payer, equity receiver, in which the notional principal is fixed. If the strike is K. the underlying swap starts at time 0=n ...
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### A relatively useless but fun question for quants and physicists

Suppose I am a trader travelling in a very fast spaceship. What kind of SDE and corresponding PDE should I jot down and work with in order to ensure that there is no arbitrage (or if there is ...
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### European Call option replication

An asset $S_t$ is evolving according to the Black-Scholes model. We want to replicate a call option on this asset by holding Delta units of the asset at every time. I use a Monte Carlo algorithm to ...