Questions about models for the valuation of option contracts.
4
votes
1answer
336 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, ...
4
votes
1answer
252 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
2answers
203 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
2answers
317 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 ...
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, ...
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 ...
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 ...
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 ...
4
votes
1answer
138 views
Longstaff-Schwartz (Least Squares Monte Carlo) applied to American Options
I'm working on an implementation in R of Longstaff & Schwartz method from the this 2001 article. I've managed to build code that replicates their prices in table 1 (p. 127), but only for the ones ...
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
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 ...
4
votes
0answers
277 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 ...
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 ...
3
votes
4answers
544 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, ...
3
votes
2answers
205 views
How do you know if if an option is priced correctly?
Besides obvious extreme examples (ie volatility going to infinity, infinite time, zero time, or zero volatility, deep OTM/ITM ) how does one gauge if an option is 'correct' or at least in the ...
3
votes
2answers
357 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 ...
3
votes
1answer
288 views
price of a “Cash-or-nothing binary call option”
I'm stuck with one homework problem here:
Assume there is a geometric Brownian motion \begin{equation} dS_t=\mu S_t dt + \sigma S_t dW_t \end{equation} Assume the stock pays
dividend, with the ...
3
votes
1answer
168 views
Sufficient conditions for no static arbitrage
In Carr and Madan (2005), the authors give sufficient conditions for a set of call prices to arise as integrals of a risk-neutral probability distribution (See Breeden and Litzenberger (1978)), and ...
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 ...
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 ...
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 ...
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 ...
3
votes
1answer
147 views
Choice of epsilon for numerical calculation of vega in binomial option pricing model
I have a binomial option-pricing model (I don't think the details of how its implemented are relevant). However, when I go to calculate vega, I am essentially running the model a second time with new ...
3
votes
1answer
287 views
Interpreting QuantLlib implied volatility numbers
I am using QuantLib to calculate implied volatilities.
I am trying to understand the calculated figures (especially, when compared to historical volatility). The calculated implied volatility numbers ...
3
votes
1answer
127 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 ...
3
votes
1answer
120 views
Foward-start option pricing
Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and is generated by $1 d $- ...
3
votes
0answers
80 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 ...
2
votes
3answers
831 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 ...
2
votes
5answers
394 views
Call vs. Put Option
I have two interrelated questions that have been bothering me for some time. I have read all the stuff online and it still doesn't make sense to me:
Let us assume:
0% interest rate (both hedge ...
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 ...
2
votes
1answer
171 views
what is the implied volatility on a basket of options
If I have 4 optionable stocks A,B,C,D and each different implied volatilies,IV-A,IV-B,IV-C,IV-D. How do get the implied volatility for a basket option on A,B,C,D where the basket weights are w-A=.6, ...
2
votes
1answer
105 views
American Option price formula assuming a logLaplace distribution?
What are $d_1$ and $d_2$ for Laplace? may be running before walking.
When I tried to use the equations provided, the pricing became extremely lopsided, with the calls being routinely double puts. ...
2
votes
1answer
97 views
Multiple Discrete Dividends
Using the recombining tree model as described in Haug's Option Pricing Forumla one can factor in multiple future discrete dividends when calculating the option value and greeks.
What's unclear is ...
2
votes
2answers
304 views
How to calculate Vomma of Black Scholes model
This source (PDF) gives the closed-form for vomma (or volga, i.e. the second derivative of price w.r.t. volatility) of the Black Scholes option pricing model as:
...
2
votes
0answers
77 views
Probability Density of Returns of Bonus Certificates
Could anyone please help me with the following?
I need to generate a histogram (resp. probability density) of returns of a bonus-certificate.
A bonus-certificate can be replicated by an underlying ...
2
votes
0answers
259 views
Can the Heston model be shown to reduce to the original Black Scholes model if appropriate parameters are chosen?
Summary
For Heston model parameters that render the variance process constant, the solution should revert to plain Black-Scholes. Closed from solutions to the Heston model don't seem to do this, even ...
2
votes
0answers
128 views
Pricing with collateral
I have been confused about many things concerning the princing of securities with collateral.
We can prove that today's price of a security( fully collateralized and within the same currency) is the ...
2
votes
0answers
64 views
Any thoughts on how Warren Buffet's B of A warrants might be “marked-to-market” by either counterparty?
It's not too long since Berkshire Hathaway got its 10-year warrants in Bank of America alongside its \$5 billion purchase of preferred stock. At the time I saw some discussion about the value of ...
2
votes
0answers
89 views
How to find the upper bound of a digital option given some market data?
Given the price of a call equals to 5 with Strike 100, please find the upper bound (sup) of the digital option with strike 105.
I am not sure about the solution, but I write the condition like this,
...
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.)?
...
1
vote
1answer
102 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 ...
1
vote
1answer
257 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
1
vote
1answer
84 views
Good Model Calibration Books/Papers for Common Option Pricing Models
I am trying to find a good book which focuses on the model calibration. I just want to know generally, what are the most common methods of model calibration(such as Black-Scholes Model, Stochastic ...
1
vote
0answers
82 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 ...
0
votes
1answer
166 views
Exotic option pricing
I'm trying to price an option with payoff $\max\{a\cdot S_t - K,0\}$ where $a$ is a known constant. Ideally I'm looking for a closed form, continuous-time solution. Where should I begin?
0
votes
1answer
147 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 ...
0
votes
1answer
85 views
Reference on SDE driven by jump processes
Are there reference on SDE driven by jump proccesses? e.g. Shepard-Nielson Model
0
votes
1answer
228 views
Which prediction market model is efficient and simple to use?
For a college project I'm tasked with implementing prediction market. Which model of it I'd better choose?
I want something useful and simple enough for other people to quickly understand and use. ...
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?
0
votes
1answer
118 views
Numerical difficulties in fitting option prices
In [1], the authors state that "Although some studies apply the curve-fitting method directly to option prices, the severely nonlinear relationship between option price and strike price often leads to ...
