Questions about models for the valuation of option contracts.

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12
votes
6answers
2k 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 for ...
5
votes
3answers
561 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 ...
4
votes
1answer
309 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 ...
6
votes
4answers
723 views

Software for decomposing structured products 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 ...
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? ...
5
votes
3answers
1k 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 ...
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 ...
6
votes
2answers
319 views

illiquid american options pricing

What are the standard methods to price american call/put options on illiquid underlyings?
7
votes
2answers
1k 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 ...
4
votes
1answer
890 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 ...
9
votes
5answers
5k 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 ...
8
votes
2answers
575 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 ...
6
votes
1answer
477 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 ...
14
votes
8answers
4k 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 ...
19
votes
0answers
560 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 ...
11
votes
1answer
989 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 ...
26
votes
8answers
2k 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 ...
10
votes
8answers
4k 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 ...