Questions about models for the valuation of option contracts.
3
votes
2answers
127 views
What mathematical characteristics are required from the asset price process in order to stay within the RNP framework?
I'm currently doing a course in derivatives pricing and I'm having some trouble wrapping my head around the sweet spot where theory meets reality in terms of Risk Neutral Pricing.
I know that the ...
5
votes
2answers
290 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, ...
10
votes
5answers
1k 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 ...
3
votes
1answer
128 views
Parameter estimation using martingale measures - include real world data?
Please note: I posted this in nuclearphynance first, but didn't get any replies.
For desks which sell exotics it is common practice (as far as I know it) to calibrate the model (Stochastic ...
4
votes
2answers
205 views
How to think about pricing this weather call option
So as opposed to the normal structure using a reference temperature and HDD/CDD, I'm looking at pricing a call option with a structure similar to the following:
Daily option on maximum daily ...
4
votes
3answers
302 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 ...
8
votes
3answers
831 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 ...
8
votes
3answers
3k views
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. ...
4
votes
0answers
278 views
ATM volatility versus OTM volatility and directional standard deviation
The forward instrument vol curve is skewed to the downside (50 delta risk reversal, 25 put, 25 call) were trading several ticks to the put).
Is there a smaller standard deviation (in price terms) to ...
6
votes
2answers
1k 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, ...
-6
votes
3answers
480 views
True or False? An option's price will always be greater than or equal to its intrinsic value
Since if the option's price is lower than its intrinsic value (eg. strike price - current stock price for puts), then an arbitrage opportunity arises from buying the option at bargain and then ...
6
votes
1answer
129 views
Should we apply practical constraints on the distribution of monte carlo paths?
to limit interest rate paths to a 'reasonable' range (if we could define reasonable). Now we calibrate log-normal skew and mean reversion monthly to robust basket of atm swaptions and in and out ...
7
votes
2answers
660 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:
...
6
votes
4answers
1k views
How does an option's time value depend on moneyness?
How does an option's time value (also known as extrinsic or instrumental value) depend on how far it is in the money or out of the money? In other words, how does the time value change as the ...
6
votes
1answer
417 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) ...
3
votes
1answer
248 views
Which approach is better for modeling option exercise strategies, rational or behavioral?
This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some ...
7
votes
2answers
1k views
Are there comprehensive analyses of theta decay in weekly options?
Are there comprehensive analyses of how much theta a weekly options loses in a day, per day?
I know what the shape of theta decay looks like, in theory, where the decay towards zero happens more ...
5
votes
1answer
209 views
How to value a floor when a loan is callable?
Certain bank loans pay a spread above a floating-rate interest rate (typically LIBOR) subject to a floor. I would like to find the value of this floor to the investor. Assume for this example that ...
9
votes
3answers
778 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 ...
6
votes
2answers
264 views
illiquid american options pricing
What are the standard methods to price american call/put options on illiquid underlyings?
7
votes
2answers
967 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
338 views
How to apply quasi-Monte Carlo to path-dependent options?
Following up on my recent question on variance reduction in a Cox-Ingersoll-Ross Monte Carlo simulation, I would like to learn more about using a quasi-random sequence, such as Sobol or Niederreiter, ...
6
votes
1answer
240 views
How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?
I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
3
votes
0answers
81 views
Analysis of Unbalanced Covered Calls
Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events.
I couldn't find any reference to this strategy (unbalanced is ...
0
votes
1answer
149 views
Does an option's price “ratio” with the underlying security price?
I'm trying to understand option pricing better.
Let's say security ABC is \$40, and a 38 PUT option with 40% implied volatility (and 90 days till expiration) is priced at X. If security ABC then ...
3
votes
1answer
111 views
What are good conditions to roll a leap further out in time?
If you're hedging with a back month / leap option, what are good underlying / market conditions to move this option out even further in time?
For simplicity, let's say you own a call with 6 months ...
1
vote
1answer
258 views
Calculating Theta assuming other variables remain the same
Is there any way to calculate theta at X day in future based solely on knowing
1) Total Current Option Price
2) Days Till Expiration
How would this be done? Thank you
4
votes
1answer
167 views
Standard Deviations out the money where options will respond to underlying asset price changes
Is there an understood way of determining how far out the money an option can be, before it starts/stops responding to the underlying asset price changes?
I usually look at the greeks, gamma, delta, ...
8
votes
1answer
271 views
Option Portfolio Risk - Volatility/Skew - practical implementation
I'm trying to improve my methods for calculating real-time US Equity option portfolio risk.
My main problem is volatility "stability" across all strikes in an option series.
The current ...
2
votes
0answers
160 views
Tian third moment-matching tree with smoothing - implementation
I was wondering if someone has an implementation of the Tian third moment-matching tree (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1030143) with
smoothing in code (e.g. c++, vba, c#, etc.)?
...
4
votes
0answers
141 views
Use of Local Times in Option Pricing
I know two applications of local time in option pricing theory.
First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
12
votes
3answers
461 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 ...
8
votes
3answers
421 views
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?
8
votes
3answers
712 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 ...
4
votes
1answer
378 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 ...
13
votes
2answers
573 views
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 ...
8
votes
1answer
178 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 ...
11
votes
1answer
731 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 ...
11
votes
6answers
2k 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 ...
2
votes
3answers
835 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 ...
8
votes
1answer
325 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 ...
2
votes
2answers
1k 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 ...
0
votes
1answer
210 views
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?
6
votes
4answers
551 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
0answers
213 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}}
...
4
votes
1answer
155 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 ...
4
votes
1answer
409 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 ...
3
votes
1answer
191 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 ...
5
votes
3answers
444 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
262 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 ...
