Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
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Is it possible to price a call option given a daily underlying returns distribution?
Apologies in advance if this problem is somewhat ill-posed. But I was thinking given the price of a call option can be formulated in terms of a implied probability density function at time $T$, would ...
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Models for tick-by-tick / high-frequency data
I've spoken to one or two persons at some market making shops, and I'm under the impression that for modelling tick data, aside from the rise of ML, a pure jump process such as the variance gamma ...
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How did Jim Gatheral come up with the SVI parameterization?
I know it has nice properties relating to Roger Lee's moment formula and the Heston model asymptotics, but I am just curious how Jim Gatheral came up with this formula in the first place. I read a ...
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Volatility Mismatch in SABR Calibration
Problem Statement
Hi, I am trying to calibrate SABR on a new asset, which is not 'forward swap rate'. While using the vanillaSABR calibration, I find the parameter 'sigma' (one of model parameters, ...
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Pricing illiquid CSO with Monte Carlo
I'm trying to price a CSO on Soyoil. The instrument is extremally illiquid.
To proceed, I simulate both leg by Monte Carlo, using the historical correlation over the 75past days and their respective ...
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Confusion about payoff for an option [closed]
My teacher said that the payoff of a put is $\mathrm{max}(K-S_T, 0)$, where $K$ is the strike price and $S_T$ is the spot price at maturity. Why isn't it $K$ if $K-S_T > 0$ and $0$ otherwise (i.e. $...
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Monte Carlo methods: Choosing the best measure
When pricing derivatives using Monte Carlo methods, we take outset in the risk neutral pricing formula which states that we need to calculate the expected value of the discounted cashflows. To do this,...
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Decomposing option payoffs [closed]
Suppose an option payoff function $$max(min(S-1, 2-S), 0)$$ To value such an option, one would decompose this function, for example, as follows: $$max(S-1, 0) - max(2S-3, 0) + max(S-2, 0)$$ Now, it ...
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Practical use of Dual Delta?
I am wondering what the practical use of the Black-Scholes Dual-Delta is?
I know it is the first derivative wrt the strike price:
$$
\frac{\partial V}{\partial K} = -\omega e^{-r T} \Phi(\omega d_2)
$$...
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Pricing non-vanilla options on EuroStoxx50 dividend futures
Liquid vanilla EuroStoxx50 dividend futures options quoted on Eurex are calls or puts whose expiries are the same as the expiry of the underlying futures contract.
Is there any "simple" ...
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Arbitrage with two puts and definition of convexity
This is concerning a common interview style question which has me confused; it has been discussed here:
How to Take Advantage of Arbitrage Opportunity of Two Options
and
Arbitrage opportunity ...
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Clarification on a Claim in Black-Scholes-Merton Derivation
In these notes: https://johnthickstun.com/docs/bscrr.pdf, towards the end of the proof of Proposition 5.2 on page 6, the author claims:
$$
\log
\lim_{n \to \infty} \Bbb{E}_\pi \left[\frac {S^*_n} S \...
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Reproducing the results in Peter Jaeckels implied volatility paper. Why is the objective function only conditioned on the initial estimate of $\sigma$
I am trying to reproduce the results in the article "By Implication" by Peter Jäckel (2010).
On page 4, for equation (3.9) of the paper, we have have
$$
\sigma_{n+1}=\sigma_n+\tilde{\nu}_n \...
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In a CRR model, find the Initial investment of the hedging strategy
Given a Cox-Ross-Rubinstein model with $T=10$, $u=1.1$, $d=0.9$,
$r=0.02$, $S_0=100$ and a European call option with Strike $K=220$,
find the initial investment of the hedging strategy.
I know how to ...
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How to Determine Parameters in a Non-recombining Binomial Tree for Option Pricing
For a CRR recombining Binomial Tree, let the underlying stock price be $S_0$ at $t=0$ and the time interval be $\Delta t$. The nodes at $t=\Delta t$ and probabilities reaching them can be written as:
$...
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Options market making process (step-by-step)
What are the steps involved in options market making?
Does it roughly follow this procedure:
Choose a pricing model, e.g. Black-Scholes.
Calibrate the model, e.g. Volatility.
Quote a bid-ask spread ...
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Empirical Evidence for Support/Resistance Levels in Martingale Price Processes and Its Impact on Option Volatility Surfaces
In financial mathematics, the martingale property often serves as an essential foundation for the stochastic processes that underlie securities pricing models. According to martingale theory, the most ...
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Delta on dividend paying equity index
we calculate the delta as change in NPV for 1% change in spot * 100. Would bumping up the forward price by same 1% produce the same results? I'm assuming F = S *exp(... ) or it's too simplifying ...
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How to modify the Heston Model such that we can modify the wings of the volatility surface?
In Heston model, if my intuition is correct, increase in sigma (volatility of volatility parameter) would increase the kurtosis and correlation factor between returns and volatility dictates the skew ...
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Cheyette Model vs Markov Functional Model
Just like to understand more about the model difference between 1d-Cheyette Model vs 1d-Markov Functional Model.
Is there a model difference betweeen these 2?
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Financial software: academia vs. real world [closed]
I am looking for resources (if they exist) that explain the differences between quant finance software in academia and the real world, or explain how quant software is implemented in practice.
For ...
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Uncertain Volatility Model - Option Pricing R code help
I am trying to price the following call option using the UVM method in R.
The code I wrote below keeps producing the same price for the min and max volatilities, which is wrong, however, I can't seem ...
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Heston Calibration - how far OTM can an option be before it's not considered ATM anymore?
I have been doing reading and supposedly implied volatility of ATM options with 1-2 week expiries are reasonable vols to use as your $V_0$ when calibrating a Heston model.
Firstly, why would it be ...
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Volatility Time and Interest Rate Time
In Sheldon Natenberg's book "Option Volatiliy & Pricing (2nd)", he mentioned that (on page 65), only trading days (roughly 252 in a year) are counted when computing vol time and all ...
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Reconstructing the CRR model knowing put and call prices
In an arbitrage-free single-period CRR model, the following options on a share are offered:
[They are all European]
(i) Call option at strike price $100$, price: $C_{0,1}=7.44$
(ii) Call option at ...
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Difference Between Option market price and Theoretical price? [closed]
So I am working on strategies that depends on the difference between Actual market price of option and price derived using black and scholes model.
For eg: Spot 19000 , strike 19200 . It is OTM call ...
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Should volatility surfaces be relatively smooth?
I have been trying to build a volatility surface with the newton-raphson method and have been using SPXW call options as my data points. I have checked my code with other calculators and have verified ...
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Option Pricing for Illiquid case
I am currently studying crypto options trading and have observed that there is often a lack of liquidity for options (such as BTC Options) on various exchanges, including Binance. In many cases, there ...
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Practical consideration for the calibration of an option pricing model
Let us say that I want to calibrate for example the Heston model to some observed prices of European call options, and that I will use some different strikes and some different maturities to do the ...
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asian geometric option valuation-- unable to get monte carlo simulation to converge to analytic value
I'm trying to price asian put options in which the averaging window begins immediately (T=0). currently, I'm trying to match up geometric averaging between my Monte Carlo simulations and my attempt at ...
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Best Method (Or Just a Good Method) of Predicting Intraday Volatility in Real Time?
I apologize if this is a stupid question, I'm a complete neophyte in academic finance but I am trying to learn.
I am trying to create an estimate of how likely indexes are to rise/fall by x% by the ...
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QuantLib Python: How to print each caplet/floorlet value, intrinsic value and time value at each fixing date?
I have the following code to price a floor (can also be used for cap), and have been computing the payoff myself, but I think QL can already do this. Since the cashflows I print out aren't correct as ...
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Can the risk neutral pdf derived from Breeden-Litzenberger Method be used to calculate vega and theta?
I have been researching volatility smoothing techniques and risk-neutral pdf.
I noticed one interesting post in
Does the risk neutral pdf that is derived using Litzenberger-Breeden Method correspond ...
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State-of-the-art grid construction techniques
I am wondering what the state-of-the-art regarding grid definition and construction, for solving PDEs using finite differences. I know some techniques are described in Duffy's Finite difference ...
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Accounting of a stock put option for Monthly % Changes
am looking to backtest a strategy of systemic put buying on an equity index (e.g SPX Index) so say a strategy of buying 1Y 90% SPX Puts rolled 1 day prior to expiry.
As opposed to only calculating the ...
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Option Payoff in Different Currencies
In the stackexchange answer Change of numeraire in options with currency exchange features
Pratically speaking, what this expresses is that these two things are the same:
Converting the payoff (which ...
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Leveraging Computational Techniques for Real-Life Option Pricing Models and Transforming Research into Utilitarian Products for Society [closed]
As a student specializing in computational finance, my passion lies in exploring the practical applications of advanced computational techniques in option pricing models for real-world scenarios. I ...
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Risk Neutral Pricing Exercise
I have the following exercise: A financial security pays off a dollar amount of $S_T^2$. Using Ito`s Lemma, what is the price today $V_t$ of this security? (S follows a Geometric Brownian Motion $dS = ...
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Conventions and Modeling of CDS Options
I am curious about the current standard conventions and modeling techniques in the CDS options market. I would be glad if someone could elaborate on the following topics:
State of the art of index ...
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Convergence in the CRR model
Under certain conditions, the option price of the CRR (Cox-Ross-Rubinstein) Binomial model converges to the Black-Scholes price as the maximal step size of the partition converges to zero (i.e. a ...
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Pricing European Call Closed Form Spread Options in Python
I am currently trying to correctly price European Call Closed Form Spread Options using Python. The main problem I am currently running into is that I have nothing to compare the option price so that ...
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Different volatility convention
In listed option's world, sometimes I see someone put different vols interchargablly, e.g.
6.7% Vol or 171 abpv or 11 dbpv
may anyone elaborate each jargon in some detail, and how and when should they ...
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When is gamma and theta in the same direction?
So, I am reading Natenberg and it says that during expiration(close to expiration), the deep in the money options will have Gamma and Theta in the same direction. This was a bit counter intuitive to ...
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Risk-neutral density versus put-call skew and open interest
I've been experimenting with the Breeden-Litzenberger formula in Python based on some code obtained here:
https://github.com/robertmartin8/pValuation/blob/master/ProbabilisticValuation/...
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Replication of a payoff with vanilla products
A lot of research has been done in the direction of replication techniques, and most of them consider the max function. I was wondering if we have an interest rate benchmark $R$, a cap $C$, a floor $F$...
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Collateral rate vs. funding rate vs. repo rate in derivatives pricing post-GFC
I am reading Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing by V. Piterbarg.
Now I have a question about the relation of the different funding rates in the paper.
$r_C$ is ...
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Pure jump process in Duffie, Pan and Singleton's paper
In page 1349 or Section 2.1 of "Duffie, D., Pan, J., & Singleton, K. (2000). Transform Analysis and Asset Pricing for Affine Jump-Diffusions. Econometrica, 68(6), 1343-1376" the pure ...
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Can you trade options with market scoring rules?
In a double-auction market, buyers and sellers are always balanced in number -- a traditional market-maker in such markets doesn't really hold any assets/take any position long-term.
However, with a ...
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Is homogeneity preserved under change of measure?
In a paper, Joshi proves that the call (or put) price function is homogeneous of degree 1 if the density of the terminal stock price is a function of $S_T/S_t$. In the paper I think Joshi is silently ...
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