Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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11 votes
3 answers
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Reference on Markov chain Monte Carlo method for option pricing?

I have to implement option pricing in c++ using Markov chain Monte Carlo. Is there some paper which describes this in detail so that I can learn from there and implement?
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9 votes
2 answers
4k 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 the following. In finite discrete Time with trading times t={1,...,T} the following are ...
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14 votes
3 answers
7k views

How does volatility affect the price of binary options?

In theory, how should volatility affect the price of a binary option? A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now let's ...
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11 votes
3 answers
2k 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 ...
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  • 509
7 votes
1 answer
2k views

Can anyone give me a practical example of pricing and calculating IV on equity index options? (i.e. using real market data)

I have been trading (mostly equity and equity index) options for a while now and I want to apply a slightly more quantitative approach to my trading - specifically, by calculating IV and incorporating ...
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  • 173
15 votes
3 answers
2k views

How to price a volatility-index option?

There exist several volatility indices, such as the CBOE Volatility Index (VIX). There are also options on such indicies. What is the best way to price a volatility-index option? Is there a simple ...
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  • 380
12 votes
1 answer
311 views

How should FX options be priced when a currency is artificially capped?

The question is inspired by yesterday's (06/09/11) historic announcement by the Swiss National Bank that it would impose a ceiling on the franc of 1.20 against the euro. I would like to know if there ...
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16 votes
3 answers
6k views

How can one compute the Greeks on VIX Futures

I am guessing the short answer to this question is "use the chain rule and linearity of the derivative," but I am looking for more specific advice on how to compute the derivatives of a VIX futures ...
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  • 2,816
18 votes
2 answers
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Duality between constant rebalanced portfolio (CRP) and corresponding derivative

One of the greatest achievements of modern option pricing theory is finding corresponding dynamical trading strategies in linear instruments with which you can replicate and by that price derivative ...
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  • 27k
18 votes
4 answers
7k views

How to solve for the implied stock lending rate given equity options prices?

When market makers price options on hard-to-borrow equities, they include the cost to borrow the underlying equity that their broker is going to charge them to sell the security short to hedge. I'm ...
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4 votes
3 answers
4k views

Why are exotic options most popular in FX?

I was reading Derman's latest blog post on Vanna Volga pricing, which, according to the linked Wikipedia article, is used mostly for pricing exotic options on foreign exchange (FX). This Willmott ...
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35 votes
5 answers
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How should I calculate the implied volatility of an American option in a real-time production environment?

There are many models available for calculating the implied volatility of an American option. The most popular method, employed by OptionMetrics and others, is probably the Cox-Ross-Rubinstein model. ...
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0 votes
1 answer
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What are the rules for quoting option prices on the market?

I have implemented a monte carlo pricer for an option. I simply don't know how many decimals I need to include in the quoted price. Can anyone please provide guidelines?
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7 votes
3 answers
756 views

Debunking risk premium via "hedging" argument? (or why even in the real world $\mu$ should equal $r$)

Since I began thinking about portfolio optimization and option pricing, I've struggled to get an intuition for the risk premium, i.e. that investors are only willing to buy risky instruments when they ...
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7 votes
2 answers
6k views

How do I estimate convergence in monte carlo methods?

I am experimenting with Monte Carlo methods. I'd like to measure/estimate convergence with a graph/chart. How do I do that? Can anyone please direct me to relevant documentation/links or even give me ...
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  • 121
6 votes
1 answer
227 views

How to scale option pricing components in regard to time

I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model. I have run into a very basic question. How should I scale the input variables in regard to time? My ...
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  • 739
15 votes
2 answers
1k views

What are important model and assumption-free no-arbitrage conditions in options trading?

In the paper "Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula" (Espen Gaarder Haug, Nassim Nicholas Taleb) a couple of model-free arbitrage conditions are mentioned which limits ...
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  • 2,049
13 votes
1 answer
646 views

Transformation of Volatility - BS

I have recently seen a paper about the Boeing approach that replaces the "normal" Stdev in the BS formula with the Stdev \begin{equation} \sigma'=\sqrt{\frac{ln(1+\frac{\sigma}{\mu})^{2}}{t}} \end{...
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  • 181
62 votes
9 answers
78k views

What are some useful approximations to the Black-Scholes formula?

Let the Black-Scholes formula be defined as the function $f(S, X, T, r, v)$. I'm curious about functions that are computationally simpler than the Black-Scholes that yields results that approximate $...
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  • 2,049
5 votes
1 answer
993 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 ...
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  • 181
5 votes
1 answer
571 views

European turbo warrants

Totally new to the world of quant finance, so perhaps this is an odd question... Does there exist an American equivalent to the German style "knock out zertifkate"? (The name might be slightly wrong....
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  • 151
18 votes
7 answers
7k views

Formal proof for risk-neutral pricing formula

As you know, the key equation of risk neutral pricing is the following: $$\exp^{-rt} S_t = E_Q[\exp^{-rT} S_T | \mathcal{F}_t]$$ That is, discounted prices are Q-martingales. It makes real-sense ...
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7 votes
3 answers
1k 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 ...
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  • 411
5 votes
1 answer
379 views

An equation for European options

So, any European type option we can characterize with a payoff function $P(S)$ where $S$ is a price of an underlying at the maturity. Let us consider some model $M$ such that within this model $V(S,\...
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  • 2,641
9 votes
4 answers
1k views

Software for decomposing payoff diagrams into plain vanilla products

Nowadays structured products (or packages) with complex payoff diagrams are omnipresent. Do you know of any software, add-ons, apps, code whatever, that enables you to enter a payoff diagram or a ...
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  • 27k
7 votes
10 answers
4k 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? ...
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  • 271
6 votes
3 answers
3k views

Longstaff Schwartz method

I try to implemente the LSM method with this algorithm but my price is always too low. By example for an American put option with the following parameters: S0 = 36, Strike = 40, rate = 6%, T = 1 ...
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15 votes
4 answers
4k 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 ...
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  • 261
8 votes
2 answers
483 views

illiquid american options pricing

What are the standard methods to price american call/put options on illiquid underlyings?
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  • 1,993
9 votes
2 answers
2k views

Which risk-free rate to use to price a bond issued in one currency but convertible into equity in another?

A convertible bond denominated in USD is issued by an Indian company (with equity traded in INR). The bond will be repaid in USD and if converted into equity in the company, the conversion price will ...
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8 votes
1 answer
1k views

Simple model for option premium (for covered call simulation)?

Given a historical distribution of weekly prices and price changes for a stock, how can I estimate the the option premium for a nearly at-the-money (ATM) option, say with an expiration date 3 months ...
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  • 800
23 votes
6 answers
29k views

What is the implied volatility skew?

I often hear people talking about the skew of the volatility surface, model, etc... but it appears to me that a clear standard definition is not unanimously in place among practitioners. So here is ...
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  • 4,453
10 votes
2 answers
2k views

Extensions of Black-Scholes model

For the Black-Scholes model my feeling is that the volatility parameter is like sweeping stuff under the rug. Are there models which improve on the volatility aspect of Black-Scholes by adding other ...
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8 votes
1 answer
689 views

How to use binomial tree for portfolio of equity products

How can I use a binomial tree to price a European option that's based on a portfolio of equity products? I have volatility and correlation matrix of all underlying products? Looking for a formula ...
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  • 447
33 votes
11 answers
17k views

Probability of touching

For a vanilla option, I know that the probability of the option expiring in the money is simply the delta of the option... but how would I calculate the probability, without doing monte carlo, of the ...
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  • 3,638
36 votes
0 answers
1k views

How to show that this weak scheme is a cubature scheme?

Weak schemes, such as Ninomiya-Victoir or Ninomiya-Ninomiya, are typically used for discretization of stochastic volatility models such as the Heston Model. Can anyone familiar with Cubature on ...
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  • 4,453
16 votes
1 answer
2k views

How do I price OANDA box options?

How do I price OANDA box options without using their slow and machine-unfriendly user interface?: http://fxtrade.oanda.com (free demo account) sells "box options": If you already know what a box ...
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48 votes
9 answers
5k views

Are there any new Option pricing models?

Back in the mid 90's I used the Black-Scholes Model and the Cox-Ross-Rubenstein (Binomial) Model's to price Options. That was nearly 15 years ago and I was wondering if there are any new models being ...
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20 votes
8 answers
15k views

Why does implied volatility show an inverse relation with strike price when examining option chains?

When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts. As a current ...
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