Questions tagged [black-scholes]

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

635 questions
48 views

Stochastic solution (mean, variance) to lognormal drift and normal volatility

I have trouble deriving the state equations for a mixture of normal/lognormal stochastic differential, namely for its a) expected mean, (b) variance, and (c) drift adjustment for LMM - libor model I ...
2k views

Forward implied volatility

Can one price accurately by only using vanilla options a derivative that is exposed/sensitive mainly to the forward volatility ? If it is impossible, why do we hear sometimes "being long a long ...
79 views

Is there a method to interpolate the volatility smile?

I have a small question of interest. During my classes at the university I have learned about the Nelson-Siegel method to fit interest rate curves. With this method you are able to determine interest ...
65 views

What are the main problems for calculating the implied volatility of in the money American put options?

As stated in the question I have a problem with calculating the implied volatility for in the money put options I have a data set of 2.6 million American style plain-vanilla call and put options. For ...
57 views

Fast implied volatility for american options

Peter Jäckel has developped a method to compute implied volatilites from option prices, called "by implication", see the papers : By Implication Let's be Rational on its website -- as well as a ...
172 views

Why do I get a curved line when I plot “implied interest rate” on the strike price?

Currently, I am working on my thesis (MSc. Finance) and I run into an interesting “phenomenon”. I have option data for a non-dividend paying stock. In class I have learned, how to calculate the ...
149 views

I have the following general SV model: $$dS = \sigma S dW_S$$ $$d\sigma = a(\sigma,t) dt + b (\sigma, t) dW_\sigma$$ $$dW_S dW_\sigma = \rho dt$$ where $a , b$ are deterministic functions of $\... 1answer 197 views Options Pricing and Mean Reversion I'm confused about the impact that a mean reverting stock price process has on the value of an option on it. Several sources say that there is indeed an impact on the price of an option: Option ... 1answer 27 views Security value based on futures contracts of a traded and non-traded assets S1 - index with dividend a, S2 - non-traded asset. A security pays off$S_{1T}S_{2T}$upon its maturity S1 and S2 are uncorrelated and follow geometric brownian motion. What is the value of ... 0answers 83 views Swaption : Bloomberg Black implied volatility quotes and pricing in the Black model I used a lot Bloomberg's VCUB for data, but never used its integrated swaption pricer "Quick Pricer for Swaptions", nor Bloomberg's "full" swaption pricer from "SWPM -OV". I am retrospectively quite ... 4answers 169 views Value of a European Call option with Infinite maturity It is a job interview question. So, what's the value of a vanilla European call option of infinite maturity, and a given strike, vol, interest rate, spot price. I think, the answer should be "zero". ... 1answer 169 views Expectation of$\frac {S_{T_2}} {S_{T_1}}$at$T_0$Is my below computation correct (assuming flat volatlity Black Scholes model, flat interest rate curve):$\mathbb{E}(\frac {S_{T_2}} {S_{T_1}}| \mathcal{F}_{T_0}) = \mathbb{E}{\frac{S_{T_0}e^{(r-\...
348 views

Suppose a put option on a stock $S(t)$ following a Geometric Brownian motion is given, with strike $K$ and maturity $T$. Let us denote its price at time $t$ by $p(t,S(t))$. Now, by no-arbitrage ...
56 views

Correlation between Two Factor Gaussian Shortrate Model and Black Scholes Model

I want to implement a two factor Gaussian Shortrate Model \begin{align} r(t) & = x(t) + y(t) + \phi(t), \\ dx(t) & = -ax(t)dt + \sigma dB_1 (t), \\ dy(t) & = -by(t)dt + \eta dB_2(t), \end{...
40 views

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 ...
61 views

Black-Scholes volatility implied by stock prices only

I was solving Problem 2.47 from T.F. Crack's "Heard on the Street". I think that the answer given in the book is not correct and I would be thankful if you tell me, where I am mistaken. Question 2....
154 views

Pricing under risk-neutral probabilities for weird derivatives?

I would really appreciate some help to value a weird derivative that I've found in an assignment: $$X=(S_{T_1}-k)^{+} = \max(S_{T_{1}}-k;0)$$ which expires at time $T_{2}$ and uses the price at ...
545 views

Is there any public data to get OIS for differal time (1d, 1W, 1M, …, 10Y)?

I want to get data of Overnight Index Swap, also known as OIS rate, there is any public why to get this always from yesterday? For example, I want to get EFFR(Effective Federal Funds Rate), I can get ...
86 views

Hedging with different volatility (Ahmad and Wilmott paper)

In their paper they show that: - if you hedge with the realised volatility, the present value of the total p&l is the difference between the option value based on the realised volatility and the ...
441 views

Interest rates forward implied volatility models

I'm trying to find out which model to use to price a pur forward volatility product named VolBond marketed by structuring desks currently. Let me introduce the products first: Example 1: You pay 100 ...
84 views

How does the Black Scholes Model Incorporate Log Prices Into Model?

I am still not understanding the link between log prices and how that is incorporated into the BS model. I understand why log(S) is assumed because it makes math easier and it prevents ending prices ...
105 views

Delta hedging pnl to recover option price

In Black Scholes framework, assuming zero interest rates and realized volatility to be same as implied volatility, gamma pnl is exactly same and opposite of theta pnl. So if I buy an option and delta ...
2k views

List of packages in R for options pricing?

What are the best packages in R or most comprehensive packages in R for option pricing and working with options? Thanks!