Questions about models for the valuation of option contracts.

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6
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0answers
272 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}} ...
5
votes
5answers
2k 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 ...
5
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3answers
193 views

Greeks: Why does my Monte Carlo give correct delta but incorrect gamma?

For a vanilla European call, my Monte Carlo method gives the right option price and delta but the wrong gamma. In particular, the value of gamma varies wildly each time I run the method. I estimate ...
5
votes
1answer
977 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 ...
5
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1answer
378 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 ...
5
votes
1answer
398 views

Risk-neutral pricing in incomplete markets

I know that in order to use the risk-neutral valuation principle, that is, pricing options as their payoff function under a risk neutral measure, one has to have a complete market. But in the ...
5
votes
2answers
427 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, ...
5
votes
1answer
614 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, ...
5
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3answers
629 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 ...
5
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1answer
409 views

Solving Black-Scholes PDE using Laplace transform

I'm trying to obtain the Laplace transform of Call option price with repect to time to maturity under the CEV process. The well known Black scholes PDE is given by $$ ...
5
votes
3answers
264 views

Option on a dice game

I am sligtly confused by this problem, although it should not be difficult. Let us roll a sigle dice. If the dice shows $n$, I receive $n$ dollars. I can buy an option to roll the die again. What is ...
5
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1answer
400 views

Is Behavioral Finance relevant to quants?

This topic has been prompted by the following question: Measuring Behavioral Finance Effects in Fund/Portfolio Manager Analysis After reading it and the comments below I started thinking whether ...
5
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1answer
2k 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 ...
5
votes
1answer
1k 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 ...
5
votes
1answer
492 views

What are the main flaws behind Ross Recovery Theorem?

Stephen Ross’ new paper claims that it is possible to separate risk aversions and historical probabilities if the Stochastic Discount Factor is transition independent using Perron-Frobenius Theorem. ...
5
votes
2answers
267 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 ...
5
votes
1answer
123 views

Normalized price process $Z(t)=\frac{\Pi(t)}{B(t)}$

If an interest rate model with the following $P$-dynamics for the short rate. $$dr(t)=\mu(t,r(t))dt+\sigma(t,r(t))d\bar{W}(t)$$ Now consider a $T$-claim of the form $\chi = \Phi(r(T))$ with ...
5
votes
1answer
151 views

Model calibration to illiquid assets when pricing options with long maturities

Let us assume one is interested in pricing an option with a very long maturity (up to 20 or 30 years) on a liquid underlying. The market won't have liquid quotes for the higher maturities. Still you ...
5
votes
3answers
2k 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 ...
5
votes
1answer
159 views

What is the stochastic differential of a general semimartingale?

By using the canonical representation of a semimartingale in Eberlein, Glau and Papapantoleon's "Analysis of Fourier Transform Valuation Formulas and Applications", on page 3: $$H = B + H^c + h(x) ...
5
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1answer
2k 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 ...
5
votes
1answer
183 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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0answers
110 views
+100

Why do people always seek finite-variance models for option pricing

For the purpose of getting fatter tails than the Guassian, I have seen people for example use $\alpha$-stable processes to model the stock. But in that case they end up using 'tempered' versions of ...
5
votes
1answer
101 views

Time value of option not always leading to an increased option value

My understanding was that as you increase the time to expiry of an option, the value of the option increases. However, I have run a bunch of scenarios and have realized that if you assume a dividend ...
5
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0answers
113 views

Basket option density in BS model

Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
4
votes
3answers
421 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 ...
4
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6answers
3k 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
226 views

Can option prices be characterised by an ODE?

If a stock price, $S(t)$, is governed by a geometric brownian motion. Is it possible to characterise the value of an option $V(S,t)$ as an ODE rather than a PDE (given $S$ is itself a function of ...
4
votes
2answers
358 views

Black-Scholes fastest computation method

What is the fastest way to numerically compute Black-Scholes-Merton option prices? I'm trying to find fastest and still precise method. Currently I'm using numerical approximation of Normal cdf with ...
4
votes
1answer
949 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 ...
4
votes
2answers
59 views

Importance Sampling - where to center the sampling distribution?

Consider a Monte Carlo (MC) approximation to a European call with BS parameters $r = 0.05, \sigma = 0.4, T = 10, S_0 = 50$ and $K = 95$. Consider the following results, each using 1M points: plain ...
4
votes
5answers
689 views

Consensus on Cauchy distribution for stock prices

What is the general consensus for using a Cauchy distribution to model stock prices? I can't find much after researching online and wonder if it has been tried and discarded. My motivation is to find ...
4
votes
2answers
307 views

Is there a contradiciton between option prices being martingales and the use of options for speculation?

It seems like there is a contradiction between the fact the option pricing is risk-neutral and the large amount of option trading that is done for speculation. Since the option is risk-neutral, a ...
4
votes
2answers
902 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 ...
4
votes
1answer
277 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
2answers
377 views

Expected value of Black-Scholes

(Apologies for any formatting mistakes) Within the Black Scholes model, given that you are estimating the volatility from historical data - and all other parameters assumed exact - one usually ...
4
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2answers
453 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 ...
4
votes
2answers
557 views

Successfull applications of Chaos Theory in Quant Finance

Do successful applications of chaos theory to quant finance exist ? While still in the university I remember some people mentioning how chaos theory and fractals could be applied in a finance ...
4
votes
4answers
3k views

How to calculate the implied volatility using the binomial options pricing model

I want to calculate IV for american options with dividends. So far I have found algorithms to calculate the option price given a volatility. Please can you point me to paper or implementation (R, ...
4
votes
1answer
77 views

Boundary conditions of PDE from SV model with stochastic interest rate

The PDE for the American put option price $P(S,\sigma ,r,t)$ is \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + ...
4
votes
3answers
105 views

Price of an asian option with squared of average payoff

Is there a closed form solution of the following price formula? Assuming $dS_t=rSdt+\sigma S_t dW_t$ under the Q dynamics $e^{-r(T-t)}\mathbb{E}_t^\mathcal{Q}[(\frac{(\int_0^T S_u du)}{T})^2]$ I ...
4
votes
2answers
2k 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
447 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 ...
4
votes
1answer
312 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 ...
4
votes
1answer
451 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
622 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
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1answer
314 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
173 views

Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?

Or simply: why do we call equivalent martingale measures as risk-neutral measures? In the utility or game theory, when we consider a person's preferences to certain outcomes, we often deal with the ...
4
votes
1answer
237 views

How does out-of-sample option pricing work in practice?

When estimating in-sample option prices, one usually estimates the structural parameters $\theta_t$ using all information up to time $t$, and then prices the option at time $t$ using the obtained ...
4
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1answer
82 views

Need for Binomial Representation Theorem

In some texts (e.g. Baxter & Rennie, Shreve I) the binomial model is first constructed using the usual backward induction argument, and it is concluded that by no-arbitrage the time $t$ value of a ...