Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
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How do you price an option on fresh corn?
I'm preparing for quant interviews, and I had this question for myself. I'm not actually trading corn options. My goal here is just to better understand how to deal with these kinds of options.
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Can call price increase in falling markets
Say SPX falls so much that there is panic and implied volatility(iv) increases so greatly that OTM call prices are increased during the fall due to high iv
In my observation in historical data this ...
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Pricing of European options on two underlying assets
Is anybody able to give the solution to the following problem?
Suppose we have two assets, each of which follows a GBM process, and where $dW_S$ and $dW_X$ are correlated $(dW_SdW_X=\rho)$.
$dS=\mu_s ...
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Pricing (Single and Double) Window Barrier FX Options
recently I have been trying to understand how to price FX options with single and double window barriers.
Could someone please recommend a source (e.g., book, article, etc.), where I can find the ...
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Continuation value definition in Longstaff and Schwartz
I am going through the paper by Longstaff and Schwartz (2001) on American-options pricing, and something got me confused.
There, in equation $(1)$ the continuation value at time $t_k$, $F(\omega; t_k)$...
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American Option Valuation - Induction algorithm
The price of an American put option is given by
$$V_k = \sup_{\tau\in\mathcal{T}, \tau\ge t_K} E\{e^{-\int_{t_k}^\tau r_sds} (K-S_{\tau})^+|\mathcal{F}_{t_k}\}$$
I found in one book the following:
$$\...
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Unable to link volatility structure to swaption pricing engine
Good morning,
I am trying to link the volatility surface to my swaption pricing engine.
...
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Black Scholes derivation: Why treat Delta as a constant?
In the derivation of the Black-Scholes equation, it is argued (e.g. in the original paper and in Hull) that
$$dV(S_t, t)=(…)dt + \frac{\partial V}{\partial S} dS_t,$$
where $V(S_t, t)$ is the value at ...
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Difference between number of stocks and number of bonds: Predictable vs adapted
Let $\nu_k$ and $\eta_k$ denote the number of stocks and number of bonds in the portfolio. According to Schweizer, we need $\nu_k$ to be predictable and $\eta_k$ to be adapted. In the text, the ...
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Change of Numeraire technique (Cross-currency models)
Hey I have problem with understanding change of numeraire technique. For example we have
$dr^d(t)=\kappa_1(\theta_1(t)-r^d(t))dt+\sigma_1 dW_1$ (under measure $Q^1$ associated with domestic bank ...
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Difference between Risk minimization and local risk minimization
According to the survey paper "A Guided Tour through Quadratic Hedging Approaches" by Schweizer the risk function is defined by
$$R_t(\phi)=E[(C_T(\phi)-C_t(\phi))^2|\mathcal{F}_t]$$
When ...
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Find the value of put option using a two-period binomial model
I've been asked to find the price of a two-month European Put Option with strike price $£40$.
The price at $S_0=£30$, this can move up to $£40$ or down to $£25$ ($1/3$ chance to go up, $2/3$ chance to ...
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Do put options experience theta/time decay?
I'm new to quant finance, and I'm confused as to whether or not European put options experience theta decay? It doesn't make sense to me that they should for a couple reasons outlined below, but ...
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Power options for pricing European claims
I have the following question:
Why would somebody be interested in the expression $E[S^\theta]$ for $\theta$ between zero and one.
The only thing I know is that this then can be somehow used to ...
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Closed form expression for $\Bbb E(\mathbb{I}_{\{S_{1,T}>S_{2,T}>K \}})$
Is it possible to calculate analytically $\Bbb E(\mathbb{I}_{\{S_{1,T}>S_{2,T}>K \}})$, using the 2-dimensional normal probability function $\Phi_2$, where $S_{1,T}$ and $S_{2,T}$ follow ...
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How to find probabilities of moves in a trinomial tree?
I'm given a non-dividend stock with price $p$ and volatility $v$ and given a European Call option corresponding to this stock.
I want to calculate the probabilities of the following moves:
$M_U = \...
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How can I simulate the barrier option call model in Python?
We have a barrier call option of European type with strike price $K>0$ and a barrier value
$0 < b< S_0$,
where $S_0$ is the starting price.According to the contract, the times $0<t_1<....
user57440
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Option pricing with risk-neutral approach
Problem
Given $Y_t$ price of a stock (no-dividents), and a derivative paying $Y_T^2$ at maturity $T$, evaluate the price of the instrument now using risk-neutral approach and check that it satisfies ...
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Choice of grid for numerical integration
I have to compute an integral involving the characteristic function for pricing options in a model and it so happens that accurate approximation seems to be mostly about putting lots of points in ...
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LIBOR Rate in Short-Rate Models
Hey I have problem with understanding the relation between short rate $r$ and LIBOR rates (which we need to calculate payoff from FRA, Caps, Swaption etc.). We know that Zero-Coupon Bond price is
$$P(...
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Option pricing using characteristic function
I'm currently on a mission trying to calculate option prices using the rough Heston model. I've found that this is usually done using the characteristic function of the model, but I must admit that I ...
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Interpreting Implied Volatility in Commodities Options
I understand that implied volatility is the expected volatility of an underlying contract in the Black option pricing model. This is easy to interpret for assets delivered at a point in time. But how ...
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Fundamental difference between stocks/bonds and options that require different pricing method
As for the pricing of stock, we can use the DCF method. For the pricing of bonds, we can also use the DCF method.
As i understand, for the pricing of stocks and bonds, to use the DCF method, we must ...
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Optimizing Options Portfolio
I’m working on a model which creates a portfolio of options. The model has an alpha from an options trade for 1 period using several different underlying stocks. Would Mean Variance optimization still ...
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Validation of XVA models
Hey what is the validation of XVA models (CVA, FVA etc)? As we know XVA calculation is rather complex problem (simulation, Valuation, aggregation) so what steps should be taken to check if the model ...
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Why is call option value same as portfolio value at all times in Black Scholes model?
Following is a part of the text from Steven Shreve Stochastic Calculus for Finance II, for pricing the European Option in Black Scholes model.
The argument is that today I start by selling a European ...
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The greeks, vanillas and digitals
Question 1: I know website’s like: https://optioncreator.com/ display the pricing and payoff graphs of regular plain vanilla puts and calls. I would like to know if there is any website that displays ...
user59094
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What is the cause of this option chain anomaly?
LAST CHG BID ASK VOL OPEN INT. STRIKE
363.15 1.35 359.80 361.40 6 12 420.00
What's peculiar is that the price is significantly higher than the ask price. The question ...
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Selling American calls before ex date vs. exercising
From reading Hull OFOD (among other references), I understand that early exercise makes sense for an American call option at time $t_n$ when $$D_n > K\Big[1-e^{-r\big(T-t_n\big)}\Big]$$
for a call ...
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Requesting for price?
Just for education purpose. Assuming I have some trading ideas that involves the use of OTC derivatives but I may not be able to put them into practice due to regulatory issues and huge minimum ...
user59094
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Volatility basics: what happens to implied volatility of stock in week of earnings and dividend payment?
Question: Imagine it is a Monday. Company A (stock you are following) has an upcoming dividend payment on Wednesday and an earnings announcement on Thursday. Company A stock is currently trading at \$...
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Python - Problem of random numbers in MC simulation
I am interested in estimating the price of a European Call Option using the Montecarlo simulation, to get a good approximation of the analytical Black Scholes formula, so a very simple task. ...
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Is it fair in an introductory stochastic calculus/derivatives pricing class to ask for the price when absence of arbitrage is violated? [closed]
Re close votes: I believe this is a fair kind of opinion-based question because it's like those ethics questions in academia se or workplace se or because it's pedagogical.
Context: I'm actually ...
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Control Variates - Option pricing
I am trying to reduce the Monte Carlo variance with Control Variates technique. In practice, I am able to reduce it with a generic European Call option, with the following formulas:
$$ Z_{CV} = \frac{...
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Can I combine the exotics for a payout?
Can I combine a one touch option(barrier lower than current price) and no touch option(barrier higher than current price), so that I get a payout immediately only if the one touch barrier is breached ...
user59094
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Option pricing when stock price follows binomial tree
Assume that the stock price is currently trading at $S_0$. It is known that the stock price follows a binomial tree, such that its price will be either $S_0e^{\theta_u}$ or $S_0e^{−\theta_d}$ over the ...
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Calibrate Local Volatility model to price quanto options
I have a Local Volatility model. I compute the LV surface $\sigma_{S}^{local}$ on vanilla option of $S$. Assume the vol of foreign exchange is constant and know, and the correlation equity/FX is known....
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Why Local Volatility model underestimate price of double no touch options
By reading this great answer, on points 2 and 3, it is stated that the Local Volatility model is not adapted to price barrier double-no-touch options.
But I don't understand exactly why. Could you ...
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Dupire pricing equation derivation vs Black Scholes PDE
I know the Dupire pricing equation is derived in similar way to Black Scholes PDE, but it is not exactly the same equation. Dupire equation reads:
$\boxed{\frac{\partial C}{\partial T} = \frac{\sigma^...
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Forward volatility smile: Local Volatility vs Stochastic volatility
I was reading this great answer: What are the advantages/disadvantages of these approaches to deal with volatility surface?
And I have the following question:
How to show that the forward volatility ...
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Correlation Spot Vol - when is it important?
I know that a local volatility model does not allow to control the correlation between Spot and Vol. I know also that the correlation Spot Vol is important for products like autocalls.
Why is ...
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What is delta of an option signaling?
In an interview I was once asked what the delta of an option was and my answer started from the fact that it is the first derivative of the option with respect to the price, and then I concluded ...
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Monte Carlo Greeks for Fixed Strike Asian Call
I am interested in pricing an European-style fixed strike asian call with payoff $\max(A(S)-K;0)$, where $A(S)=\frac{1}{n}\sum_{i=1}^nS(t_i)$ is a discrete arithmetic average and $K$ is the strike ...
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Finite difference methods with discontinuity in the payoff function
I have implemented a finite difference scheme for pricing options using a Black-Scholes-like model. I tested my implementation on a call option, and found that it gave extremely inaccurate results. I ...
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Black-Scholes Portfolio
In the black-scholes model, the hedging portfolio is given (in some textbooks) by
$$\Pi_t = V_t - \Delta S_t,$$
i.e., the portfolio consits of a long position in the option $V$ and $\Delta$ units of ...
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How is Emanuel Derman's implied tree model implied volatility skew derived?
I am reading Emanuel Derman's paper Patterns of Volatility Change. The section, Implied Volatility In The Sticky Implied Tree Model has the linear skew approximation near the old underlying $S_0$
$$\...
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Reference for path dependent options
I want to study path dependent options for which I am following the book Paul Wilmott on Quantitative finance.But here I dont find the detailed explanations or derivations for the various PDEs .So is ...
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Approximating second derivatives at boundary of finite difference scheme
The Question
I am implementing a finite difference scheme for the Heston-Hull-White PDE:
\begin{align}
\frac{\partial u}{\partial t} &= \frac{1}{2}s^2v\frac{\partial^2 u}{\partial s^2 } + \frac{1}{...
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Difference in pricing of American call and put
In Paul Wilmotts quantitative finance books he says that the the value of an American option satisfies the following
$$
\frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2 \frac{\partial^2V}{\partial ...
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Impact of Discrete and linear dividends on Local Volatility model
I am trying to understand the assumptions and weaknesses of a Dupire Local Volatility model.
If dividends are assumed linear, is it a problem for model calibration? If yes, why?
Why would large values ...
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