Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
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How to get the fair value for an option with variable strike?
I'm dealing with a plain vanilla written put but my strike is linked to this formula:
$$K=(7 \cdot EBITDA\cdot Net Debt)\cdot [\%P]$$
where
EBITDA = EBITDA of the company as of the last closed and ...
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Pricing look-back option
I have the monthly price data of a stock starting from December 2020 and I am considering a EU style look-back option issued in December 2020. The payoff at maturity of the look-back option is given ...
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Closed form / analytical solution for bespoke (but vanilla) Option
Question:
I want to derive closed form expression (similar to the Black Scholes formula for a call price) for the payoff below. I would like to do it from first principles starting with Expectations ...
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Floor vs Receiver Swaption with Equal Strike
Let's say we have the following two instruments.
A 5x10 floor (5-year floor, five years forward) with a 4% strike on 1-year SOFR and
A 5 into 5 European receiver swaption (right to enter into a 5-...
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Risk-neutral option pricing under distribution assumption
For simplicity assume zero interest rates in the following.
Given the price of a (European) put option with strike K and maturity T at time point t. $P_t(K, T)$ for a given underlying S with values $...
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Kou model — solving PIDE for European and American options in Python
Toivanen proposed$^\color{magenta}{\star}$ a method to solve the partial integro-differential equation (PIDE) with a numerical scheme based on Crank-Nicolson. In particular, he proposed an algorithm ...
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Kou model - can't reproduce prices of European Option from Toivanen and Forsyth [duplicate]
I have implemented the Kou option model for pricing vanilla option. I have checked that my program can replicate the price of the option in the original paper of 2002. However, when I use it to price ...
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What will be the payoff equation of a GBPUSD European Exotic option/FX forward with Notional in USD [duplicate]
Given the currency pair , GBPUSD with
spot price as $S_t$ at time $t$, Strike price as $K$, $I$ is an indicator function indicating if GBPUSD is below the "Knock-in-Rate" at expiry, $L$ ...
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Price a contingent claim with payoff $(S_{1T}-S_{2T})^+$ at time $T$
Two stocks are modelled as follows:
$$dS_{1t}=S_{1t}(\mu_1dt+\sigma_{11}dW_{1t}+\sigma_{12}dW_{2t})$$
$$dS_{2t}=S_{2t}(\mu_2dt+\sigma_{21}dW_{1t}+\sigma_{22}dW_{2t})$$
with $dW_{1t}dW_{2t}=\rho dt$....
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How can I price this option? [closed]
In the Black-Scholes model, I want to price the so called Butterfly option, where the payoff $P(x)$ is the following function: $P(x)=0$ if $0\leq x\leq 40$, $P(x)=x-40$ for $40\leq x\leq 60$, $P(x)=-x+...
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Replication of the payoff of a chooser option
With numerical examples, how can the payoff of a chooser option be replicated with European call and put options?
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Fitting volatility using SABR
I have been working on generating a volatility surface for options on SOFR futures with the help of the SABR model. I am running into some trouble for low strikes in particular, in that I cannot seem ...
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How are VIX options priced in a mean-reverting framework?
If a trader assumes that the VIX follows a mean-reverting process like the Orstein-Uhlenbeck process, how would they price this non-martingale asset? My intuition tells me a trader would use doob-...
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Satisfying put-call parity in Monte Carlo option valuation
I am trying to price European call and put options on a stock using the Monte Carlo method, given some dynamics for the underlying that may or may not have a closed-form solution (e.g. Black-Scholes, ...
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A naive approach to choose a strike
The idea is to choose a strike base on the premium and historical data to have maximum profit.
For example a selling a (European) call.
$$Profit = Premium_K - (S(t) -K)^+$$
Replacing $(S(t) -K)^+$ for ...
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American option pricing using path integrals
I am writing a brute force code in python that implements the path integral formalism for the American put option, the goal being to obtain its price at given a price $S_0$ of the underlying asset.
...
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what is the point of SABR model as an interpolation tool if we can already observe the whole vol cube from the market
on BBG and other data providers, it is common that you can find the whole vol surface/cubes. What is the point of the SABR model as an interpolation tool? why cannot people just linear interpolate the ...
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How to calculate option premium stop loss if underlying reaches a certain value near the strike price given the current implied volatility
I have sold a put option. The market is likely to open negative on Monday, the expiry of option is on Thursday. I have a certain stop loss level in my mind to exit this position if the index reaches ...
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Pricing an option with a certain payoff
Suppose an option with a payoff function
$$ \max((1+k)S_1,kS_2) $$ where $S_1, S_2$ are stock prices and $k>0$ is a constant value.
To value such an option, one would decompose this payoff function ...
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Theta using black scholes when time to maturity approaches 0
When time to maturity tends to 0, like on expiry day, denominator $\sqrt t$ in becomes 0 and the first term in the formula becomes large enough to make theta of the contract more than its premium. How ...
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Why is it said that Girsanov’s theorem destroys the tractability of the process which is undesirable for quantitative finance applications？
I am reading the paper "Risk-neutral pricing techniques and examples" by Robert A. Jarrow et al., and it is said that Girsanov’s theorem destroys the tractability of the process which is ...
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How to calculate profit loss curve of a put option [closed]
I am using the black scholes method to calculate the premium for selling put option using the py_vollib package in Python. I can calculate the premium for a put option that has an arbitrary strike. ...
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Monte Carlo option pricing
Can someone please confirm if I understood this correctly.
The Monte Carlo method for pricing path-dependent options essentially gives you a multitude of price processes, which you use to determine ...
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Do different hedging strategies affect the theoretical pricing of options in one period binomial model?
I just started my financial maths master and was introduced to binomial option pricing for European options.
I am slightly confused by the derivation as I saw a different version. Some straightly get ...
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In the paper "By Implication" by Jaeckel, he says that put-call parity should never be used in practic
In this paper by Jackel (2006), on page 2, he writes:
The normalised option price $b$ is a positively monotic function in $\sigma \in[0, \infty)$ with the limits
$$
h(\theta x) \cdot \theta \cdot\left(...
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Ito formula and confusion with the differential operator $d$
Thanks for visiting my question.
Im am currently working on this paper (https://arxiv.org/abs/2305.02523) and I am stuck at page 21 (Theorem 14 proof).
First these SDE's were defined:
\begin{align*}
...
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Pricing a callable bond in a minimal way
I am looking for a minimal way to price callable bond from a defaultable issuer. The idea is to assume that we are in a deterministic world (i.e no volatility).
I tried a methodology but I am not sure ...
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Could a phoenix autocall be priced by a snowball option with zero coupon plus expectation of coupons received in knock out observation dates?
I know that coupons in the phoenix autocall can be received in each observation date if the underlying price in that date does not touch down the knock-in barrier and receiving periodic coupons is ...
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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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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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answer
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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 ...