Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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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 ...
0 votes
0 answers
73 views

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, $L$ ...
0 votes
3 answers
91 views

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 ...
1 vote
3 answers
214 views

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-...
9 votes
2 answers
1k views

How we can derive the PIDE of double exponential jump-diffusion model (Kou model)?

I'm working in double exponential jump-diffusion model known as the Kou model with following form, under the physical probability measure $P$. $$ ‎\frac{dS(t)}{S(t-)}=\mu‎‏ ‎dt+\sigma ‎dW(‎t)+d(\sum_{...
0 votes
1 answer
86 views

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 $...
0 votes
0 answers
123 views

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 ...
2 votes
1 answer
196 views

Questions about the replicating portfolio in the binomial model

I'm starting to teach myself quantitative finance and I've got several questions (marked in bold) regarding the replicating portfolio of a security in the binomial model. I'm following, among others, ...
1 vote
2 answers
451 views

Configuring barrier option in Quantlib-Python

Is there a possibility to configure the period the barrier is active, using Quantlib for python? Namely to set up the start and the end dates we compare the spot vs the barrier. If we look at quantlib-...
1 vote
1 answer
118 views

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 ...
2 votes
0 answers
54 views

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 ...
0 votes
0 answers
117 views

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 $dW_{1t}dW_{2t}=\rho dt$....
0 votes
1 answer
126 views

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+...
0 votes
0 answers
28 views

Double no-touch option brokerage(s) [closed]

Are there any retail brokers that you are aware of that offer double no-touch options specifically?
28 votes
0 answers
630 views

Is there a relationship between Risk Neutral Pricing framework and Nash Equilibria?

Based on the Fundamental Theorem of Asset Pricing, the risk neutral price of a contingent claim on an asset in a liquid, arbitrage free market can be determined by switching to an equivalent $Q-$ ...
3 votes
1 answer
832 views

Forward starting options concepts

Consider $t_0<t<T$, with $t_0=0$ (today date) and the standard payoff of a vanilla forward starting call option, $F_{t,T} = (S_T - S_t\cdot K)^+$, with strike $K$. If the price of this option is ...
0 votes
1 answer
56 views

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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52 views

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 ...
0 votes
1 answer
41 views

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 ...
4 votes
2 answers
543 views

Simulation scheme for SABR beside the standard Euler discretization

QUESTION: Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics? Simulation that will withstand even for high volatilities....
0 votes
0 answers
35 views

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-...
0 votes
0 answers
54 views

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, ...
0 votes
0 answers
69 views

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 ...
2 votes
1 answer
113 views

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, ...
2 votes
1 answer
170 views

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 ...
0 votes
0 answers
37 views

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. ...
9 votes
2 answers
717 views

Change of numéraire for two risky assets without bank account (Margrabe’s formula?)

I am considering two risky assets following the usual correlated GBM given by $$\frac{\mathrm{d}S^{(i)}_t}{S^{(i)}_t}=\mu_i\mathrm{d}t+\sigma_i\mathrm{d}W^{(i)}_t,\quad i\in\{1,2\}$$ with $$\mathrm{d}...
0 votes
1 answer
128 views

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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0 answers
32 views

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 ...
4 votes
3 answers
2k views

Probability of an Option maturing In-the-money vs. Volatility

How will the probability of an option ending up in the money change if the volatility of the underlying stock increases? Intuitively, I think the answer to this is that if volatility goes up the ...
1 vote
2 answers
444 views

Converting implied volatilities into digital option prices

I have Black and Scholes (1973) implied volatilities computed and I would like to convert these IVs to digital option prices using a Black and Scholes type of formula, I can't find a formula to do ...
0 votes
2 answers
151 views

Best tool to find an optimal option? [closed]

I like to sell uncovered put options, using my valuation of the company as the strike price. I'm looking for a tool that takes stock identifier and strike price as input and outputs the optimal ...
-4 votes
1 answer
127 views

Black Sholes Options Pricing Clarification Questions [closed]

I am interested in pricing American Call and Put Options using BSM and I am new to exploring options prcing. I have some questions here that would really remove the confusion I have on how to more ...
0 votes
1 answer
76 views

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 ...
1 vote
1 answer
129 views

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 ...
2 votes
0 answers
70 views

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 ...
0 votes
1 answer
77 views

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. ...
0 votes
0 answers
71 views

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 ...
2 votes
0 answers
69 views

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*} ...
2 votes
0 answers
70 views

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(...
7 votes
2 answers
275 views

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 ...
1 vote
0 answers
74 views

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 ...
0 votes
0 answers
97 views

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 ...
2 votes
5 answers
2k views

How to price an exchange option using B&S framework?

Consider a market composed by two stocks whose prices $X$ and $Y$ are given by B&S diffusion: $$dX_t= \mu X_t dt+ \sigma X_tdW_t$$ $$dY_t= \mu Y_t dt+ \sigma Y_tdB_t$$ Supposing the market is ...
1 vote
1 answer
254 views

What's the price of a lookback call option in the arbitrage-free CRR-model?

If we consider the CRR-model in two periods, i.e. T=2. Let $S^1$ be the risky asset with $S_0^1=100$ and $S^0$ the bond with $S_0^0=1$. Furthermore, we assume the model is arbitrage-free with $y_b=-0....
0 votes
1 answer
44 views

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 ...
3 votes
0 answers
137 views

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 ...
1 vote
0 answers
90 views

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 ...
0 votes
1 answer
63 views

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 ...
0 votes
0 answers
25 views

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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