Questions about models for the valuation of option contracts.
8
votes
2answers
588 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 ...
2
votes
5answers
403 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 ...
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 ...
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:
...
3
votes
1answer
121 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
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 ...
0
votes
0answers
47 views
earnings reports and option pricing
Let's assume that company XYZ reports earnings in a 0% interest rate environment and the option expires shortly after earnings. And there is a 50% chance the earnings are good (an upmove) and 50% bad ...
6
votes
10answers
1k 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
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 ...
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 ...
4
votes
2answers
146 views
Is drift rate the same as interest rate in risk-neutral random walk when using Monte Carlo for option pricing?
When using following risk-neutral random walk
$$\delta S = rS \delta t + \sigma S \sqrt{\delta t} \phi$$
where $\phi \sim N(0,1)$.
Now when a text mentions drift = 5% does that mean that interest ...
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 ...
4
votes
1answer
253 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 ...
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
6
votes
1answer
172 views
Upper bound concerning Snell envelope
Consider a non-negative continuous process $X = \left (X_t \right)_ {t\geq 0}$ satisfying $ \mathbb E \left \{ \bar X \right\}< \infty $ (where $ \bar X =\sup _{0\leq t \leq T} X_t $) and its ...
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 ...
5
votes
1answer
141 views
How to derive the formula of a European Libor call option in a Libor Market Model?
I am struggling with the following two mathematical statements. The first is from the book "Term-structure Models: A Graduate Course - Damir Filipović" Suppose we have a deterministic function ...
3
votes
1answer
289 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 ...
4
votes
4answers
666 views
How to price a calendar spread option?
How do you price calendar spread options, that is, options on the same underlying and the same strike but different times to maturity?
Clarification: I'm interested in the pricing of a a CSO ...
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 ...
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. ...
12
votes
2answers
550 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
951 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 ...
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 ...
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, ...
4
votes
2answers
321 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 ...
5
votes
0answers
100 views
Replicating portfolio and risk-neutral pricing for interest rate options
For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing ...
14
votes
3answers
608 views
When do Finite Element method provide considerable advantage over Finite Differences for option pricing?
I'm looking for concrete examples where a Finite Element method (FEM) provides a considerable advantages (e.g. in convergence rate, accuracy, stability, etc.) over the Finite Difference method (FDM) ...
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 ...
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 ...
10
votes
7answers
2k 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 ...
6
votes
2answers
337 views
How to transform process to risk-neutral measure for Monte Carlo option pricing?
I am trying to price an option using the Monte Carlo method, and I have the price process simulations as an inputs. The underlying is a forward contract, so at all times the mean of the simulations is ...
18
votes
0answers
460 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 ...
15
votes
6answers
5k 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 ...
0
votes
1answer
144 views
Question on OptionMetrics: “Strike Price times 1000” differs too much from Index price
I have a question regarding the strike price that is given on OptionMetrics. My goal is to primarily retrieve options prices of a specific maturity with strike prices that are 20% in-the-money, ...
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 ...
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 ...
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 ...
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?
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 ...
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
4answers
545 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, ...
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 ...
9
votes
5answers
2k 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 ...
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,
...
5
votes
2answers
589 views
How does one go from measure P to Q(risk-neutral) when modeling an asset paying dividends?
I am really having a terrible time applying Girsanov's theorem to go from the real-world measure $P$ to the risk-neutral measure $Q$. I want to determine the payoff of a derivative based an asset ...
4
votes
1answer
215 views
Reference on Electronic volatility trading [duplicate]
Possible Duplicate:
Looking for a recommendation for a real life volatily trading book.
I recently came in contact with a quant desk that traded volatility. The discussion only highlited my ...
4
votes
4answers
1k views
How to get greeks using Monte-Carlo for arbitrary option?
Let's assume I have an arbitrary option that I can price using Monte-Carlo simulation. What is the general approach (i.e. without relying on specific option type) to calculating the greeks in this ...
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 ...
