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

learn more… | top users | synonyms (1)

11
votes
3answers
3k views

Is there an all Java options-pricing library (preferably open source) besides jquantlib?

I am looking for an all-java implementation of black scholes, preferably open source. I found jquantlib and quantlib (C++). Any other recommendations? The jquantlib site seems to be down. I'd prefer ...
6
votes
10answers
2k views

Using Black-Scholes equations to “buy” stocks

From what I understand, Black-Scholes equation in finance is used to price options which are a contract between a potential buyer and a seller. Can I use this mathematical framework to "buy" a stock? ...
1
vote
1answer
199 views

Testing Black Scholes Analytical Options Pricer

I've written some code to calculate European option prices using the Black-Scholes analytical method. Can somebody recommend a good way to test that code? I have looked at option pricers online like ...
0
votes
2answers
427 views

Why the implied volatilities calculated are so different

I Calculated facebook option(expired in 12/4/13) Implied Volatility with the Bisection Method. The program will be attached at the end. The results for different strike prices are so different: ...
3
votes
2answers
273 views

Black-Scholes and Fundamentals

So basically $dS_t=\mu S_tdt+\sigma S_tdWt$ and $\mu=r-\frac12\sigma^2$ I have just been thinking about this later equation. This is very interesting because it ties together risk-free ...
0
votes
1answer
311 views

Doesn't a perpetual option contradict the Black-Scholes framework?

A standard example when learning to price American options is the perpetual American put. This is a put that has no expiry (or you can consider T = infinity). The standard solution prices this using ...
0
votes
1answer
184 views

volatility Table and BS formula

assume I have implied FX volatility Delta-Term table from broker. I have time noticed as 2M, 3M. what do I have to put into BS formula, is it 2/12 or "count the business days"/"daycount basis"? I am ...
5
votes
1answer
1k views

Taylor series expansion (Volatility Trading book) explanation sought

I am currently reading Volatility Trading, I have only just started, but I am trying to understand a "derivation from first principles" of the BSM pricing model. I understand how the value of a long ...
4
votes
5answers
839 views

How to improve the Black-Scholes framework?

Since the distribution of daily returns are obviously not lognormal, my bottom line question is has BS been reworked for a better fitting distribution? Google searches give me nada. The best dist ...
2
votes
1answer
222 views

What are $d_1$ and $d_2$ for Laplace?

What are the formulae for d1 & d2 using a Laplace distribution?
14
votes
2answers
2k views

How do we use option price models (like Black-Scholes Model) to make money in practice?

In quantitative finance, we know we have a lot of option price models such as geometric Brownian motion model (Black-Scholes models), stochastic volatility model (Heston), jump diffusion models and so ...
7
votes
4answers
1k views

Methods for pricing options

I'm looking at doing some research drawing comparisons between various methods of approaching option pricing. I'm aware of the Monte Carlo simulation for option pricing, Black-Scholes, and that ...
-2
votes
2answers
277 views

BS and delta hedging questions

I have two related questions concerning Black Scholes and delta hedging. I thought about this two questions, but I could not come up with an answer, so maybe you guys & girls can help me: If an ...
4
votes
2answers
1k views

Basket option pricing: step by step tutorial for beginners

I would like to learn how to price options written on basket of several underlyings. I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in ...
25
votes
8answers
3k views

Option pricing before Black-Scholes

According to the Wikipedia article, Contracts similar to options are believed to have been used since ancient times. In London, puts and "refusals" (calls) first became well-known trading ...
4
votes
1answer
465 views

Black-Scholes American Put Option

Here is my question: This is a question about Black-Scholes model, but it may be applicable to more complicated models. Throughout the discussion, the strike price $K$, interest rate $r$ and ...
2
votes
0answers
79 views

Changes to option valuation for dollar-pegged underlying

In Russia, options on futures on the RTS index are priced in points instead of currency, with points being directly related to the value of the US dollar such that, for example, if the dollar rises, ...
1
vote
0answers
178 views

Pricing a Power Contract derivative security

I'm trying to price a "power contract" and would appreciate guidance on the next step. The payoff at time $T$ is $(S(T)/K)^\alpha$, where $K > 0$, $\alpha \in \mathbb{N}$, $T > 0$. $S$ is ...
3
votes
3answers
345 views

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 ...
6
votes
1answer
191 views

Prove or disprove “If at least 10% of an option's value is time value, it has a delta less than 90”

"If at least 10% of an option's value is time value (ie. time value >= 0.1*call price), it has a delta less than 90". In practice and after doing many tests with an option pricing calculator, this ...
3
votes
4answers
1k views

Ways of treating time in the BS formula

The Black-scholes formula typically has time as $\sqrt{T-t}$ or some such. My questions: What is the granularity of this? If we treat $t$ as the number of days, then logically on the day of expiry, ...
7
votes
1answer
295 views

When pricing options, what precision should I work with?

I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and ...
4
votes
1answer
679 views

Can American options with no dividends and zero risk-free rate be treated as European?

Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the ...
1
vote
1answer
712 views

What precision do I need to calculate implied volatility?

I'm developing a software to calculate the implied volatility of an option using the Black & Scholes formula and a trial-and-error method. The implied volatility values I get are correct, but I ...
5
votes
2answers
371 views

A few questions about signs of the Greek letters

Rho is the partial derivative of the value of call option, $C$, w.r.t the riskfree interest rate $r$: $$\rho \equiv \frac{\partial C}{\partial r}$$ In the standard B-S formula this term is positive, ...
4
votes
3answers
398 views

Is it possible to demonstrate that one pricing model is better than another?

Take the classic GBM (geometric Brownian motion) model for equities as an example: ds = mu * S * dt + sigma * S * dW. It is the basis for the classic ...
7
votes
1answer
339 views

Simulating the joint dynamics of a stock and an option

I want to know the joint dynamics of a stock and it's option for a finite number of moments between now and $T$ the expiration date of the option for a number of possible paths. Let $r_{\mathrm{s}}$ ...
6
votes
2answers
3k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
8
votes
2answers
1k views

Why doesn't Black-Scholes work in discrete time?

I have a question considering Financial markets in discrete Time: One of the main theorems in discrete time is: In finite discrete Time with trading times t={1,...,T} the following are equivallent: ...
10
votes
2answers
2k views

Why a self-financing replicating portfolio should always exist?

According to my understanding the derivation of the Black-Scholes PDE is based on the assumption that the price of the option should change in time in such a way that it should be possible to ...
8
votes
1answer
787 views

How to 'calibrate' simple pricing models for equity index options and equity options?

I am interested in doing some research on plain vanilla equity options and equity index options. I have historical data for these options. I also happen to have market maker 'fair price' (bid and ask) ...
6
votes
1answer
3k views

What is a self-financing and replicating portfolio?

I try to understand the derivation of the Black-Scholes equation based on the "constructing a replicating portfolio". From mathematical point of view it looks simple. We assume that: Stock prices ...
6
votes
2answers
2k views

How to extrapolate implied volatility for out of the money options?

Estimation of model-free implied volatility is highly dependent upon the extrapolation procedure for non-traded options at extreme out-of-the-money points. Jiang and Tian (2007) propose that the ...
9
votes
3answers
1k views

What tools are used to numerically solve differential equations in Quantitative Finance?

There are a lot of Quantitative Finance models (e.g. Black-Scholes) which are formulated in terms of partial differential equations. What is a standard approach in Quantitative Finance to solve these ...
1
vote
2answers
1k views

Black Scholes and Monte Carlo implementations in Java [duplicate]

Possible Duplicate: Is there an all Java options-pricing library (preferably open source) besides jquantlib? Can anyone recommend a library with an implementation of Black Scholes and Monte ...
7
votes
1answer
1k views

How should I estimate the implied volatility skew term when calculating the skew-adjusted delta?

I'm trying to come up with the implied volatility skew adjusted delta for SPY options. I'm working with the following formula: Skew Adjusted Delta = Black Scholes Delta + Vega * Vol Skew Slope. I ...
15
votes
3answers
3k views

Why hold options when you can dynamically replicate their payoff?

When holding vanilla options, you can cancel out, theoretically, all risk with dynamic (delta) hedging. Then you earn the "risk free rate of return". Why would you make such a portfolio when you can ...
6
votes
2answers
489 views

Vanilla European options: Monte carlo vs BS formula

I have implemented a monte carlo simulation for a plain vanilla European Option and I am trying to compare it to the analytical result obtained from the BS formula. Assuming my monte carlo pricer is ...
4
votes
1answer
561 views

Better understanding of the Datar Mathews Method - Real Option Pricing

in their paper "European Real Options: An intuitive algorithm for the Black and Scholes Formula" Datar and Mathews provide a proof in the appendix on page 50, which is not really clear to me. It's ...
5
votes
3answers
569 views

Black-Scholes No Dividends assumption

I am doing some research involving black-scholes model and got stuck with dividend-paying stocks when evaluating options. What is the real-world approach on handling the situations when an underlying ...
10
votes
5answers
1k views

How to conduct Monte Carlo simulations to test validity of Black Scholes for a specific option?

In reference to the original Black Scholes model, what approach is best to test the model in a rigorous way? Is there a standard approach that can accomplish this in a reasonable amount of time? ...
10
votes
3answers
4k views

What are the main limitations of Black Scholes?

Pls explain and discuss these limitations, and explain which models can I use to overcome these limitations. Alternatively, provide examples of how to modify the original Black Scholes to overcome ...
8
votes
1answer
390 views

What are the main differences in Jump Volatility and Local Volatility

Is a JV model simply Local Vol + Jump Diffusion? If so, it seems logical that an existing JV model be able to be used for valuation of both Vanilla and Exotic options. Is this true? Does a Local ...
4
votes
4answers
531 views

Expected Growth

The model assumption of the Black-Scholes formula has two parameters for the geometric Brownian motion, the volatility $\sigma$ and the expected growth $\mu$ (which disappears in the option formulae). ...