# Tagged Questions

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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### Basic question about Black Scholes derivation

In the derivation of the Black Scholes equation, the value of the portfolio at time $t$ is given by $$P_t = -D_t + \frac{{\partial D_t}}{{\partial S_t}}S_t$$ where $P_t$ is the value of the ...
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### Do Bond Put Dates always fall on Coupon Dates (for non-zero coupon bonds). Calculation rules for Coupon Dates

This may not be the most appropriate SE site to ask this question, but I can't seem to find a better place to ask, so here goes: Do Puttable Bonds' put dates always fall on Coupon Dates? When they ...
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### Eurodollar Options Stike Price > 100 bps

Looking at Eurodollar IR options market data coming down from CME, I can see a whole host of options where the strike is > 100 bps. My understanding in this case is that puts will always be in the ...
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### Which approach is better for modeling option exercise strategies, rational or behavioral?

This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some ...
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### Monte Carlo and PDE results are different for a Call Option!

Okay so this might be a fairly trivial question but I'm having an issue with valuing a call option using both a Monte Carlo method and a PDE method. When I started I first used the parameters: Spot =...
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### Find call and put volatilities using ATM, Risk reversal and Butterflies volatilities

I have to plot the implied volatility surface for EUR/USD. So, my goal is to produce something like that, from put delta 10 to call delta 10: Searching for informations, I found that I could find ...
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### Black-Scholes formula proof, without stochastic integration

I've looked into many books at my academic library, and very often it goes like this: Brownian motion Then, stochastic integration (Itô's formula etc.) Application: Black-Scholes formula for price ...
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### How to get Correlation using Options data?

I can calculate the "Implied Beta" using implied volatility for the option stock, and implied volatility for the market (VIX). Is there any way to calculate also the correlation without performing a ...
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### Mean reversion time estimation

I am new to mean reversion trading, and I would like to get some good references about how to estimate the time it takes to a mean reverting process to cross its long term mean.
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### Short volatility strategy using strangles

For a short volatility strategy using option strangles, is it better to target a fixed premium to earn? Or a fixed vega? Objective is to maximise the return/risk (sharpe) of the strategy. Any help ...
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### Daily option data

I am wondering where I can pull daily (hourly, by-the-minute, etc. even better) option data for a particular underlying. I would prefer a database I could scrape through and API, but would not mind ...
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### Option pricing, origin of formula $\Pi( t,X)= E^{\mathbb{Q}}\left[e^{-\int_{t}^{T}r_s\,ds} X| \mathcal{F}_t\right]$

Imagine a model with stock prices and dividends of these stocks, as well as a market bond with associated short rate process. It is known that this model is arbitrage-free if there exists an ...
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### Black Scholes Formula, drift term

In the formula, the stock return is modelled as a brownian motion that is a drift + a stochastic term, ok I get that. But the drift term is then modelled as r - volatility ^ 2 / 2. I am not sure how ...
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### Exercise on American call option and dividends

Consider an americal Call option on an underlying paying dividends. Then it is often argued that it is only optimal to exercise right before the dividend is paid out, otherwise one will not exercise. ...
### How do I prove that $\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$?
I am trying to prove that $$\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$$ where $P(K,T)$ denotes the put option price with maturity $T$ and strike $K$ for some stock $S$. Assuming interest ...