Questions about models for the valuation of option contracts.

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Valuation of barrier options in Jump diffusion model

I am trying to evaluate the value of a Barrier option using Monte carlo method. The stock follows a jump diffusion model. I am using the method described in Metwally and Atiya. The authors describe ...
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1answer
92 views

How would you price this kind of derivative?

I am somewhat familiar with options but am wondering how to price calls/puts on this one: European exercise "Jumps" in underlying may occur Takes physical delivery upon exercise (is this even ...
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176 views

Exchange rate model and Martingales

In exchange rate model explanation, "...If under the domestic risk neutral measure $Q_d$, the process $X(t)$ satisfies $\displaystyle \frac{dX(t)}{X(t)}=\sigma dZ_d(t)$ Since $Z_d(t)$ is ...
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32 views

Discretization Schemes

I am working with two correlated SDE's and I was wondering if I could use two different discretization schemes for them. Is there maybe a reference of this being done? And can something be said about ...
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3answers
65 views

What is the effect of dividend yield being greater than the risk-free rate to American options pricing?

Even though dividends are discrete, literature often makes the assumption of continuous dividends (mostly in the case of indices but the individual stocks as well). The dividend yield denoted by q is ...
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36 views

How do options models incorporate sticky strike/delta?

Do options models such as Heston, SVI or others handle sticky strike,delta etc... I am interested in simulating how IV across all strikes can be impacted based on changes in spot. What is a ...
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26 views

Real-World Cash Account Implementation and Return

Often in financial math, the concept of the risk-free cash account, with return R, is invoked as an instrument for calculating prices - when constructing an option-replicating portfolio, for example. ...
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59 views

Underlying changes impact on implied volatility

What are some valid techniques that can be used to simulate how changes in the underlying are most likely to impact implied volatility along with the skew of all strikes for options with the same ...
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1answer
89 views

Selling an American call option early

I understand it is never optimal to exercise an American call option early. [1] [2] However, here are my two contradictory thoughts about selling an American call option early. Assumptions I can ...
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1answer
74 views

Fitting stochastic variance distributions to index return data

I want to calculate option prices based on a realistic distribution of the underlying. The underlying is a liquid index such as Eurostoxx50. I think of two aproaches, both of them incorporate ...
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1answer
144 views

How to price a Swing Option?

I'm working in the commodity market and I've to price Swing Options with MATLAB, preferably with finite element. Has anyone already priced these kind of derivatives? I'm thinking about using the ...
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2answers
94 views

Pricing Principle 1

In Tomas Björk's Arbitrage Theory in Continuous Time (or here), $\exists$ this Pricing Principle. Is the one in red supposed to be the proof of the Pricing Principle 1? Or merely an intuitive ...
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115 views

Divergence between binomial pricing and monte carlo simulation for vanilla european call?

I notice a divergence in my own code, but it's evident even in public code: http://www.thalesians.com/finance/index.php/Knowledge_Base/Finance/Option_Pricing_in_Python_and_Simple_English Pricing a ...
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1answer
94 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
88 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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1answer
118 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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1answer
115 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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62 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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2answers
97 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
64 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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44 views

Is it possible to graph the option price with respect to the greeks

Is it possible to graph a European option's price as a function of say, its delta? I've been wondering this since, for example, for a call, the option price is given by $$Se^{-q*t}\Phi (d_1) - ...
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2answers
416 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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3answers
121 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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2answers
120 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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Price of portfolio with target volatility

Consider the following: We have two assets, S1 and S2, and with each asset is associated a volatility, v1 and v2, respectively. Now let's say v1 < v2, and we want to create a portfolio of S2 and ...
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38 views

Credit Spread - pricing Option and Fixed Income

hi how do you handle credit spread 1. For Option with Equity underlying 2. For Fixed Income/Bond I understand there're two options: a. Expected Loss from Probability of Default & Recovery Rate ...
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82 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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61 views

America option early exercice boundary via Monte Carlo simulation

I am trying to calculate an american option price via the simulation of the early exercise boundary using the method presented in this document: Monte Carlo Method For pricing a put Option. I have ...
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1answer
108 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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60 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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48 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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116 views

Java Implied Volatility Solving

After using RQuantLib and RCaller from Java I am desiring a bit more speed on my implied volatility calculations (for anyone who has used this knows it is quite slow). I need to price a large number ...
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1answer
193 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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58 views

EMM in incomplete markets

The simply put question is as follows: do we need to restrict ourselves to EMM exclusively when pricing European contingent claims (=option payoffs) even if markets are incomplete? In particular, a ...
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85 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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1answer
142 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
77 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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2answers
166 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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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
178 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
146 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
111 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
114 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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2answers
269 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
258 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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177 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
186 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
131 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
167 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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277 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 ...