Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
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Pricing Different Strike Put With Call Option Price
How do we find the implied volatility from the price in a call option and apply it to another option without a calculator? Or is there actually a better way?
For example, given a 25-strike 1.0-expiry ...
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Importance sampling for Monte Carlo with local volatility in practice
I am given a diffusion with a local volatility to price barrier options:
$$dX(t)=X(t)\mu dt+X(t)\sigma(t,X)dW_t$$
I want to use Importance Sampling to price barrier options "far" out of the ...
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Cash balance sign in hedging portfolio
Consider a derivative which depends on $n$ assets with price vector $X=(S^1,\dots,S^n)$. The derivative value $V_t$ is given by the function $v(t,S)$, so that the hedge ratios for the hedging ...
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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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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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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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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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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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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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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 $P$.
$$ \frac{dS(t)}{S(t-)}=\mu dt+\sigma dW(t)+d(\sum_{...
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Risk-neutral option pricing under distribution assumption
For simplicity assume zero interest rates in the following.
Given the price of a (European) put option with strike K and maturity T at time point t. $P_t(K, T)$ for a given underlying S with values $...
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Questions about the replicating portfolio in the binomial model
I'm starting to teach myself quantitative finance and I've got several questions (marked in bold) regarding the replicating portfolio of a security in the binomial model. I'm following, among others, ...
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Configuring barrier option in Quantlib-Python
Is there a possibility to configure the period the barrier is active, using Quantlib for python? Namely to set up the start and the end dates we compare the spot vs the barrier.
If we look at quantlib-...
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what is the point of SABR model as an interpolation tool if we can already observe the whole vol cube from the market
on BBG and other data providers, it is common that you can find the whole vol surface/cubes. What is the point of the SABR model as an interpolation tool? why cannot people just linear interpolate the ...
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Kou model - can't reproduce prices of European Option from Toivanen and Forsyth [duplicate]
I have implemented the Kou option model for pricing vanilla option. I have checked that my program can replicate the price of the option in the original paper of 2002. However, when I use it to price ...
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Price a contingent claim with payoff $(S_{1T}-S_{2T})^+$ at time $T$
Two stocks are modelled as follows:
$$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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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-$ ...
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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 ...
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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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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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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....
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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)^+$$
Replacing $(S(t) -K)^+$ for ...
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Volatility Mismatch in SABR Calibration
Problem Statement
Hi, I am trying to calibrate SABR on a new asset, which is not 'forward swap rate'. While using the vanillaSABR calibration, I find the parameter 'sigma' (one of model parameters, ...
CommunityBot
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Heston Calibration - how far OTM can an option be before it's not considered ATM anymore?
I have been doing reading and supposedly implied volatility of ATM options with 1-2 week expiries are reasonable vols to use as your $V_0$ when calibrating a Heston model.
Firstly, why would it be ...
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American option pricing using path integrals
I am writing a brute force code in python that implements the path integral formalism for the American put option, the goal being to obtain its price at given a price $S_0$ of the underlying asset.
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Change of numéraire for two risky assets without bank account (Margrabe’s formula?)
I am considering two risky assets following the usual correlated GBM given by
$$\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}...
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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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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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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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
$$
h(\theta x) \cdot \theta \cdot\left(...
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Likelihood ratio and pathwise sensitivity method for coupled SDEs
I have two coupled SDEs
\begin{align*}
dS_t=rS_tdt+V_tdW_t^{(1)},\\
dV_t=aV_tdt+b(V_t)dW_t^{(2)},\\
\end{align*}
where $W_t^{(1)}$ and $W_t^{(2)}$ are independent Brownian motions, initial input data ...
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Could a phoenix autocall be priced by a snowball option with zero coupon plus expectation of coupons received in knock out observation dates?
I know that coupons in the phoenix autocall can be received in each observation date if the underlying price in that date does not touch down the knock-in barrier and receiving periodic coupons is ...
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Pricing a callable bond in a minimal way
I am looking for a minimal way to price callable bond from a defaultable issuer. The idea is to assume that we are in a deterministic world (i.e no volatility).
I tried a methodology but I am not sure ...
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How to price an exchange option using B&S framework?
Consider a market composed by two stocks whose prices $X$ and $Y$ are given by B&S diffusion:
$$dX_t= \mu X_t dt+ \sigma X_tdW_t$$
$$dY_t= \mu Y_t dt+ \sigma Y_tdB_t$$
Supposing the market is ...
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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....
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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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