Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
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Which process is the most commonly used for modeling stock prices?
I'm thinking of writing a master's thesis about pricing options using Levy processes, but I wonder if these processes are actually used for modeling stock prices or not (and which specifically)? And ...
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answers
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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 ...
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What does "convergence" in Monte Carlo simulation mean?
I have read about convergence in terms of MC simulation for derivative pricing, but I am not clear on what it exactly means.
Let us suppose I price an option 100,000 paths twice and both result in the ...
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answer
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volatility of a mid curve option
Question:
When checking the volatility surface for, let's say, a swaption, where the the option expires in 1Y and the underlying starts in 1Y and ends in 5Y, one would check the volatility surface ...
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Effect of volatility on the delta of a call option
In the book 'Dynamic Hedging', Nassim Taleb writes:
...
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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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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 ...
8
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illiquid american options pricing
What are the standard methods to price american call/put options on illiquid underlyings?
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Bermudan Swaptions - Payer vs. Receiver (LGM)
There is abundant literature discussing the pricing of Bermudan swaptions and the relevance of single-factor Markov-functional models (e.g. LGM) versus multi-factor market models (e.g. LMM).
From a ...
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Implied volatility and greeks for american option with discrete dividends
What methods are available to calculate IV and greeks for an american option with discrete dividends, and how do they compare?
Should I use Roll-Geske-Whaley and solve for a given option price?
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Derivation of Stochastic Vol PDE
A couple questions regarding stochastic vol PDE derivation. Following Gatheral, a general stochastic vol model is given by
\begin{align*}
dS(t) & = \mu(t) S(t) dt + \sqrt{v(t)}S(t) dW_1, \\
dv(t) ...
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recent developments in American options?
I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem.
Is there any development in pricing American options during 2005-2016? (based ...
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How to price a futures spread option?
Let's say I have two futures contract $F_1(0,T)$ and $F_2(0,T)$ on two different correlated underlyings.
If I assume that both underlying follow a GBM with volatility $\sigma_1$ and $\sigma_2$ ...
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answers
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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? ...
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Problems with local volatility models (vs stochastic volatility models)
Why is pricing with local volatility models are problem with exotics, mainly due to "the volatility surface is the market's current view of volatility and this will change in the future meaning the ...
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Find a formula for the price of a derivative paying $\max(S_T(S_T-K),0)$
Develop a formula for the price of a derivative paying
$$\max(S_T(S_T-K))$$
in the Black Scholes model.
Apparently the trick to this question is to compute the expectation under the stock measure. So,...
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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 ...
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answers
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Multithreading Monte-Carlo pricing in QuantLib for a single product
I've been actively using QuantLib for structured product pricing using Monte Carlo. Due to the fact that at a great deal of paths are often needed and one needs to speed up the calculation and all ...
7
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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 ...
7
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2
answers
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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 ...
7
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answers
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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 ...
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answers
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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 ...
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Does Black Scholes need to assume no arbitrage?
Since Girsanov's theorem guarantees a risk neutral measure for Geometric Brownian motion, by the fundamental theorem of asset pricing there can be no arbitrage. So, why does the model assume no ...
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How to use a stochastic volatility model to price a quanto option
I want to price a quanto option using a Stochastic Volatility model (like Heston model, 1993).
Normally, what we do is:
Calibrate the stochastic volatility model,
draw a binomial tree consistent ...
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answers
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The Upper Bound of an American Put Option
I have just read the following paragraph (in bold) and have a question on the upper bound of an american put option:
http://www.sharemarketschool.com/option-valuation-upper-and-lower-bounds-part-...
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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
$$
\frac{1}{2}\sigma(x)^2x^2\frac{\...
7
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answers
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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, ...
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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 ...
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Interpretation and intuition behind the Put-Call symmetry under the Heston Model
I am currently working on a report regarding the put-call symmetry relations under the Heston model. I did all the math and managed to prove the relations using PDE approach. However, I wish to have a ...
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Black-Scholes vs Black equation
Why is Black used for interest rate options pricing instead of Black-Scholes? Why are we more interested in Future rates instead of Spot rates when it comes to interest rate options? Basically, why ...
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Greeks for binary option?
How to derive an analytic formula of greeks for binary option?
We know a vanilla option can be constructed by an asset-or-nothing call and a cash-or-nothing call, does that help us?
Wikipedia states
...
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SABR calibration: simple explanation and implementation
I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets.
How would you explain the process and its implementation in simple steps? Any web ...
7
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1
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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 lack ...
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answers
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What are some beginner quantitative option trading strategies?
I'm new to quantitative trading, with good knowledge in finance and coding (mainly Python, Java, R, etc).
I would like to know if there are any basic quantitative option trading strategies that can ...
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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 ...
7
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Realised variance under simple rough volatility model
Using the Mandelbrot-Vann Ness representation of fractional Brownian motion in terms of Wiener integrals, increments of the logarithm of realized variance $v = \sigma^{2}$, under the physical measure $...
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Option pricing with dependent risk factors
I'm a bit stuck with the pricing of an option where the underlying stock is correlated to an additional process.
Setting: Assume that we have a probability space where under $Q$ the dynamics of the ...
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1
answer
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When pricing options, which day counting conventions should be used to calculate time to maturity?
In most option pricing textbooks, time to maturity is given as a convenient figure such as 6 months (T=0,5).
In practice how do you effectively calculate time to maturity given today's date and the ...
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answers
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How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?
I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
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How to determine the risk-neutral measure in a Heston model?
To clarify, I'm quite familiar with the risk-neutral pricing framework, and I know one can efficiently Monte-Carlo a Heston model via the non-central $\chi^2$ distribution approach. But so far we're ...
7
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answers
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Valuating Prepayment on Loans- Which models are favorable?
I have some trouble in choosing the right method/model for the valuation a prepayment option on a loan (in General).
So far I had some ideas about valuatiing it via a simple PV-method but there ...
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answer
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Should we apply practical constraints on the distribution of monte carlo paths?
to limit interest rate paths to a 'reasonable' range (if we could define reasonable). Now we calibrate log-normal skew and mean reversion monthly to robust basket of atm swaptions and in and out caps....
7
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1
answer
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implied volatility and strike price
Assume for simplicity that the expiration time of an option is $1$ the initial stock price is $1$ and there is no dividend yield and the risk free return is $0$.
How is it possible to show that the ...
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Likelihood ratio and pathwise sensitivity method for coupled SDEs
I have two coupled SDEs
\begin{align*}
dS_t=rS_tdt+V_tdW_t^{(1)},\\
dV_t=aV_tdt+b(V_t)dW_t^{(2)},\\
\end{align*}
where $W_t^{(1)}$ and $W_t^{(2)}$ are independent Brownian motions, initial input data ...
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Has a closed-form formula for the collateral choice option been found?
The collateral choice option problem has been formulated in e.g. Fujii and Takahashi (2011), Piterbarg (2012) or Antonov and Piterbarg (2013), as the computation of an expectation of the following ...
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Intuition behind the Carr and Wu (2014) static hedging for ordinary options
Let $(S_t)_{t \geq 0}$ be the price of an underlying asset, $r$ be the risk-free rate of return, $q$ the dividend yield, $C_t(K,T)$ is the price of a call option written on $S_t$ at time $t$ with ...
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How can put options be more expensive than call options in an efficient market?
I noticed that for some securities, puts were more expensive than calls (with same expiration). For example, suppose the underlying security is trading at 50. A put with a strike of 45 is more ...
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Option Price vs. Implied Volatility
I was doing an exercise on investigating the relationship between European Call option price and its volatility. I was asked to compute $\frac{\partial^2C}{\partial \sigma^2}$ and find out the domain ...
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Hull-White model applied in practice
I'm reading about the Hull-White model, I understand the math behind it and logic but what I am struggling to understand is how it's actually used in practice ? How can we combine it with technics ...
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Where can I find a clear explanation (brief derivation) of N(d1) and N(d2)?
Where can I find a good explanation (perhaps with a brief derivation) of N(d1) and N(d2) from Black-Scholes? Just trying to understand the general idea about these 2 probability functions and how they ...