Questions about models for the valuation of option contracts.

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155 views

Does a delta hedged short option guarantee profit of extrinsic value at expiration?

If a trader shorts an option and dynamically delta hedges to ensure the delta is equal to 0 if that option expires out of the money does the trader profit that options extrinsic value at the time of ...
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2answers
93 views

Joint distribution from expectations

Given two random variables $X$ and $Y$ and let $K$ be a constant value. Assume the expectation $\mathbb{E}[X(Y-K)^{+}]$ is given for all possible values of $K\geq 0$. Is there a way to derive the ...
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443 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 ...
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139 views

Intuitive understanding of Black-Scholes pricing

The Black-Scholes formula entails market completeness, so the price of an option is only the cost associated with dynamically hedging the option. Where does this cost come from? I don't see how ...
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232 views

The option values are different from two r package - foptions,rquantlib

The results are very different.I know the code from quantlib and the result of quantlib seem right(close to market price). Is there anyone know why the value from fOptions is so large or fOptions used ...
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421 views

calculate gamma value using finite difference method

I try to use the finite difference method to get the approximately gamma value, but there is an issue I can't solve. First, I set $h$ to 1 basis point of underlying asset value, but the result is not ...
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1answer
79 views

Sample size and historical correlation matrices

I was wondering whether any literatures existed on how to properly estimate correlation matrices from historical data. Obviously the entire procedures allows a lot of leeway. The frequency of ...
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565 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 ...
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180 views

Is there any other way to measure option pricing model performance than proximity to market prices?

Short version Why do we take market prices as the prices to be estimated and predicted? The common answer is efficient markets hypothesis as in "Market agents do their best effort given their ...
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140 views

american option and cash dividends

Can someoe help with this : What is the precise arbitrage argument demonstrating that the price of an american option should be continuous around an ex-dividend date? Thanks
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141 views

Pricing binary options with kernel density estimation

Suppose I have a large enough set of prices of an asset, from which I can extract the following function: $f:T\to\mathcal{D}$, where $T$ is a fixed finite set of time intervals (say, 1 minute, 2 ...
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176 views

Valuation of Cox-Ross-Rubinstein Model

We have a Cox-Ross-Rubinstein model with parameters $u$ ("up"), $d$ ("down") , $r$ (interest rate) and $q$ (equivalent martingale probability) $(q=(1+r-d)(u-d)^{-1})$ . We have a contingent claim with ...
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126 views

A question about pricing convertible bond with two different underlying assets

I have a question regarding the pricing of convertible bond. If I value the convertible bond with two different underlying assets, how can I incorporate two volatility and the correlation in the ...
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93 views

American Swaption Pricing with PDE discretization

So I am still trying to price an american swaption. (MC approach here: American Swaption Pricing with Monte-Carlo method) I've found in Paul Wilmott, The mathematics of financial derivatives, a PDE ...
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1answer
362 views

American Swaption Pricing with Monte-Carlo method

I want to price an American swaption but I am not sure about what I am doing. Tree methods and PDE discretization seem difficult to adapt to a swaption. I am trying a Monte-Carlo approach. (in ...
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1answer
94 views

Simple pricing example confusion

This it taken from "Heard on the Street", Section B. Consider a market with $0$ risk-free rate, no transactions costs etc. The IBM stock costs \$75 and does not pay dividends. Design a security ...
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170 views

How to price this option without using BS framework

We have a stock at price 1 dollar which pays no dividend. Also we assume zero interest rate. When the price hits $H$ dollars for the first time where $H>1$, we can exercise the option and receive 1 ...
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2answers
93 views

Efficient numerical approaches for pricing American Options with multiple sources of noise

I am looking for efficient numerical approaches for pricing American options when two or more sources of noise are involved (the simplest case coming to mind would be the Heston Model) Eventhough I ...
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318 views

Pricing an american style option on a bond future

what is the good way to pricing american option on bond future? From bonk fixed income securities 3rd by Tuckman, I understand how to pricing European option on bond future, but I still have no clue ...
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54 views

Incorporating a stochastic correlation structure into a multi-factor model

I am considering extending a multi-factor fixed income stochastic model (e.g. LIBOR-Market) to use stochastic correlation matrices instead of determinstic ones. For pricing instruments with short ...
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3answers
254 views

How to hedge a derivative that pays the reciprocal of the stock price?

1) Suppose S is the stock price, how to hedge a derivative that pays $1/S_t$ at time $t$? 2) Suppose there will be a dividend of amount $d$ between $t$ and $T$, how to hedge a derivative that pays ...
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2answers
188 views

Options with a stochastic strike

Do options where the strike itself is a stochastic process exist? If they do - what are the motivations for such a product and where is it used ? Example: Call-Option with stochastic strike: ...
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1answer
177 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 ...
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1answer
143 views

Effects of random-generator-choice on derivative's price

There is a plethora of pseudo-random-generators out there. Some of them are definetly better and some of them severily underperform. My standard tool is Mersenne Twister - when I need to generate ...
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1k views

Calculate volatility from call option price

Given call option price, what is the simplest formula to get the volatility value ? Test Data: ...
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1answer
296 views

Places to make quant code/tools publicly avaliable

Over the years I have developed several tools - including pricing, optimization and calibration tools - most in VBA, C# and C++ I would like to make them publicly avaliable. Aside from putting up my ...
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226 views

Algorithmic Trading Model Calculation and Stale Data

I'd like ask everyone a more concurrency programming but definitely quant-finance related question. How do you deal with staleness of data in market hours as quote ticks are streaming and your model ...
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1answer
208 views

Call option on a Mutual Fund

I am trying to price a call option on a mutual fund. Given the lack of market implied data, I am going to estimate the fund´s expected volatility using as a reference its historical volatility ...
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1answer
351 views

Implied probability density (Question 2 - Applications and Interpretation)

Using the second derivative of the Call-Option-Price one can try to recover the pricing density. Formally: Assuming a constant interst rate $r$ and also not making any assumptions on the model ...
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1answer
512 views

Implied state price density (Question 1 - derivation of the formula)

I came upon the term "implied state price density" in a couple of papers. As far as I understand the concept one basically tries to extract the "pricing density" from the market data. For the sake ...
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415 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 ...
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198 views

Practical implementation of Least Squares Monte Carlo (tweaks and pittfalls)

The Longstaff-Schwartz LSM approach is nowadays ubiquitous(at least in the academic literature) in pricing path dependant derivatives. Up to now I have mostly worked with lattice methods. My ...
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1answer
819 views

Asset-or-nothing Option Valuation in the Black and Scholes model

In standard Black-Scholes Model, compute the price of an asset-or-nothing put and asset-or-nothing call options. Write down the put-call parity relation between the asset-or-nothing call and put ...
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85 views

Pricing options with two assets

I'm studying for a test and am stuck on this practice question: With interest rates equal to 0, two different stocks $S_1$ and $S_2$, both valued at \$1 today, can be worth \$2 or \$0.50 at some ...
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201 views

How are quants able to verify whether their calculated prices are any good

This question is related to the discussion on Model Validation Criteria However it appeard to be very high level to me and I would like to go more into detail. Not working at a pricing desk the ...
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405 views

Price an option and find a replicating portfolio

I got stuck on the following question whilst learning about basic option pricing. A stock is valued at \$75 today. An option will pay \$1 the first time the stock reaches \$100 in value, which it ...
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165 views

why is the BNS model the way it is

what I am puzzled about is, why dont we instead of having \begin{equation} dX_t = \sqrt{V_t} dB_t - (\frac{1}{2} V_t^2-r-\lambda\Phi(\rho)) dt - \rho dZ_{\lambda t}\nonumber \end{equation} we just ...
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227 views

Basket Option weight sensitivity calculation

I am looking to find/estimate the "greeks"/option price sensitivities/derivatives for a basket option situation. In specific the change in price of a put option associated with a change in weight of a ...
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163 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 ...
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1answer
187 views

binary tree options pricing model with dividend value - How should I discount the option at?

the expected value of the option given the next period up, down values is: $ Pexp = (p Price_{next, up} + (1 - p) Price_{next, down})/R$ where p is defined as $p = \frac{\exp(-r \times \Delta t) - ...
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147 views

What information about the stochastic process is available from path-dependent options?

Assume the stock follows a process, which is defined by the following stochastic differential equation $$\frac{dS}{S}=r(t)dt+\sigma(S,t)dW,$$ so that the stock price process has local volatility. ...
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338 views

Is it wrong to use 'real world' probabilities for option valuation?

Is it wrong to use 'real world' probabilities for option valuation, even when the market is not liquid enough to delta hedge the option? My instinct is that it is wrong, because the time value of ...
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1answer
144 views

Derivation of the Stochastic Vol PDE

I'm trying to follow the derivation of the stochastic vol pde for an option price - as given in Gatheral (The vol surface), Wilmott on Quant Finance and many other places. As usual one starts off with ...
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65 views

Multivariate interpolation for estimating FDM in-between grid points

After implementing some FDM to price some option, there are gaps between our grid points that may be of interest. From reading around, it appears common to use bilinear interpolation to estimate ...
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3k views

Value of American Call vs Value of European Call when using implicit finite differences

I calculated values for put options (european and american) using the implicit finite difference method and compared them to black/scholes values. The values for american put options are higher than ...
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1answer
161 views

How does Vega of a call/put behave under the Black-Scholes model?

I have two questions. I would prefer a reference if possible. Is the value of vega bounded for $\sigma\in [0,\infty)$? (I assume so, I imagine it goes to 0 as $\sigma$ go to infinity.) Are there any ...
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2answers
160 views

Time-zero price of two specific contingent claims

I am unsure how to start with the following problem. I have two contingent claims where contingent claim (1) pays $\int_0^T S_u du$ and contingent claim (2) pays $(\log S_T)^2$ at time $T$ Now I ...
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416 views

Price of a down-and-out call in terms of European call

If $EC(S_0, K, \sigma, r, T)$ represents the price of a European call option with strike $K$, expiry $T$, initial price $S_0$, volatility $\sigma$ and where the constant interest rate is $r$, then I ...
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320 views

a good book on option pricing from theoretical and practical aspect

This is the situation someone I know is in: She has good understandings of stochastic calculus and the very basics about black-scholes and binomial model, but nothing more. Her background is in ...
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380 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 ...