# Questions tagged [black-scholes]

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

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52 views

### Pricing with-profit/smoothed bonus annuity using Black-Scholes

Would this be possible? Subsequently, would the pricing of such an annuity be somewhat similar to pricing a lookback option?
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### School project about Black Scholes with stochastic volatility

In a university project I am looking at Black Scholes model with a stochastic volatility. I’m still not quite sure about my focus (I am in the beginning 'Idea phase'). I want to explain the theory ...
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### Black-Scholes formula with deterministic interest rate and dividend yield

Does any one have the Black-Scholes formula for a European call with time-dependent but deterministic interest rate and dividend yield ?
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### B-S Put Option Formula: Derivation using expected value under Q

I have been working on an old problem in one of my finance classes and, since no solution has been provided and I won't be able to contact my teacher anytime soon, I was hoping I could ask you guys to ...
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### Any Simple Way to Prove Black Scholes Type Identies?

A certain complicated option pricing formula results in products of Black Scholes $N$ components like this: $-p_1N(d_1)N(d_6)+p_sN(d_2)N(d_5)>?0$ where $p_s>p_1$ Trying to find a simple way ...
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### BS Implied Volatility under Normal returns

If I use theoretical prices under a normal valuation model, and I estimate their implied volatility using BLACK SCHOLES implied volatility, do I'll get corresponding log normal volatility?
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### Question about Merton model to estimate default probability and recovery rate of the company

I recently come across Merton's model to estimate the default probability and recovery rate of the company. Here is the inputs ...
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### Distribution of realized volatility for stock prices from a GBM

If you generate random stock price paths according to a GBM with daily increments, what will be the distribution of the realized volatility? Assume that the realized volatility is measured over daily ...
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### Option Delta Calculation - Local Vol Model vs Black-Scholes Model

I am looking to get the greeks for option chain. Which model does work better for greeks calculation especially the delta. I am having issue with the Black-Scholes Model Delta since it always ...
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### Derivation of Black-Scholes for a derivative on a stock that pays continuous dividends, and the derivative pays continuous cashflows

I need help with the derivation of Black-Scholes PDE. The condition is that the derivative is written on a stock that pays dividends continuously (dividend yield D). Additionally, the derivative pays ...
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### Calculating the risk free interest rate, or the continuously compounded yield on a T-bill, at any given time

I'm working on a program using the Black-Scholes model to price options over time. I need to be able to derive the risk free interest rate, and found this while researching: In theory, r is a ...
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### Delta hedging an option with earlier expiry

The answer here states: For instance a volatility product that would expire at 10:42 am on a random day would be off term. One that expires at the same time than a major listed contract would ...
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### Swaption : Bloomberg Black implied volatility quotes and pricing in the Black model

I used a lot Bloomberg's VCUB for data, but never used its integrated swaption pricer "Quick Pricer for Swaptions", nor Bloomberg's "full" swaption pricer from "SWPM -OV". I am retrospectively quite ...
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### How can I graph futures options profit/loss when the options have different underlyings?

Consider a portfolio of vanilla SPX monthly options that consists of two components, a SEP 2019 3000 Call and a DEC 2019 3000 Call. It's easy to graph these as they both share the same independent ...
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### Calculation of Conditional Expected Value and Pay-Off Diagram

I have a stock with mu 6% and sigma 20% following a random walk and I would like to to calculate the Conditional expected Value of the stock in 10 states with equal probability (10%). Meaning, I would ...
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### How is a LIBOR Market Model volatility skew determined?

LIBOR based interest rates are derived from the prices (supply / demand) of swaptions, caps and floors. These prices are generally quoted in yield vols. Their prices are given by the Black formula. ...
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### Different scaling conventions for greeks

I have been following this tutorial (http://gouthamanbalaraman.com/blog/value-options-commodity-futures-black-formula-quantlib-python.html). It says in the conclusion and I quote:It is worth pointing ...
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### Interpretation of drift parameter $\mu$ in GBM

Currently studying Ito's calculus. Looking on the GBM model: $\frac{d S_t}{S_t} = μ dt + \sigma d B_t$ we end up on the expected stock price at time t: $E[S_t]=s_0 e^{\mu t}$.What does actually $\mu$ ...
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### What is Dual Delta?

I understand that it is the partial derivative of option price with respect to strike. What is it used for though? What does your dual delta signify?
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### SPY American option Greeks and Premium

I am trying to replicate Ivolatility.com's option calculator for a client. Here's the example Using standard Black Scholes model, I can replicate the exact calculations if there is no dividend. With ...
Is there a way to go from this $$\ln S_t=\ln S_0+(\mu-\sigma^2/2)t+\sigma W_t$$ $$\ln S_t\sim N[\ln S_0+(\mu-\sigma^2/2)t, (\sigma^2)t]$$ To the Black-Scholes partial differential equation?