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Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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How to calculate sigma in order to calculate delta? [closed]

I am calculating option delta using py_vollib.black_scholes ...
Titu's user avatar
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0 answers
186 views

Longstaff & Schwartz algorithm - Python: American option cheaper than European option

I have implemented the Longstaff & Schwartz algorithm for pricing American Option in Python, but I ran into an issue while doing some experiments: sometimes, for the same option, I get a higher ...
Noomkwah's user avatar
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37 views

Future Implied Price from Option Implied Distribution

Been reading on option implied distributions and understand that this can be transformed into a confidence interval/fan chart showing the implied future price. Was wondering how I could go about doing ...
nzc's user avatar
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1 answer
167 views

How to and What is the price of an American call option for non-dividend stock?

I want to know how to price an American call option for non-dividend stock (with concrete and simple binomial pricing model, with risk neutral assumption). I understand that for an European call ...
TJT's user avatar
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3 votes
0 answers
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Option pricing boundary condition

I am currently working on this paper "https://arxiv.org/abs/2305.02523" about travel time options and I am stuck at Theorem 14 page 20. The proof is similar to Theorem 7.5.1, "...
Valentin's user avatar
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2 votes
1 answer
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Pricing PDE of Asian option by Shreve

I am currently working on "Stochastic Calculus for finance II, continuous time model" from Shreve. In chapter 7.5 Theo 7.5.1 he derives a pricing PDE with boundary conditions for an Asian ...
Valentin's user avatar
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1 answer
121 views

Implied Distributions from forward prices

I understand that the common way to arrive at an implied distribution for an underlying is through the price of its call options as per the Breeden-Litzenberger formula. I am wondering if its possible ...
nzc's user avatar
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3 votes
1 answer
238 views

Computing Derivative Security with Change of Numeraire

Under Black-Scholes, price a contract worth $S_T^{2}log(S_T)$ at expiration. This is a question from Joshi's Quant Book (an extension question). Ok, so I solved this with 3 different methods to make ...
jmac's user avatar
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2 votes
1 answer
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Deep vs "shallow" calibration of option pricing models

I am currently investigating the application of deep learning in calibrating option pricing models, specifically, models of rough volatility, such as rBergomi. While there is a lot of research on ...
dasfobia's user avatar
0 votes
1 answer
236 views

Breaking down gamma PnL by time

Let's say in one day time, underlying price S goes up by $2.4. Then the gamma PnL should be $\frac{1}{2}\gamma_0 (2.4)^2$. Let's assume that in every hour the underlying goes up by $0.1. Then how do ...
crr1210's user avatar
2 votes
1 answer
194 views

How does the interest rate affect the implied volatility of options, especially ITM?

What would be a good reference to understand how the interest rate (r) or dividend yield (q), and I guess the differential between the two, affect the implied volatility of the options? If I look at a ...
jim mako's user avatar
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1 answer
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What accounts for the difference between these two option strategies?

Same underlying, same strike, same expiration. One is a covered call, the other is cash secured put. These are screenshots taken from a website. As you can see, they are similar, but the max win ...
Carlos's user avatar
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1 answer
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Thinking about time value of an option

In addition to Wikipedia, YouTube and other internet sources, I'm reading Timothy Crack's "Basic Black-Scholes: Option pricing and trading". Most of these sources suggest that it is fairly ...
salanfaer's user avatar
1 vote
1 answer
95 views

General Binomial Method for option pricing

I am reading the book "Principles of Corporate Finance" 12th edition by Brealey, Myers and Allen. In the 21st chapter on Option pricing, they discussed the General binomial method for option ...
user471651's user avatar
0 votes
1 answer
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Different notations for times variable in Haug's book

I am reading the book by Haug, 2007 on the pages 186-188 one can find the Turnbull and Wakeman approximation for arithmetic avarage rate option. The approximation adjusts the mean and variance so ...
Nick's user avatar
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1 answer
1k views

Bloomberg terminal option data calculation

EDIT based on the answer provided, I have followed, but still I cant match the bbg data with my calculations, could some advise how to match the bloomberg Price given the data? ...
Skittles's user avatar
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1 answer
117 views

Derivation in Jaeckel's "By Implication" paper

In this paper by Jaeckel (2006), he derives the asymptotics for the option price $b$ as: \begin{align*} \lim_{\sigma \to \infty}b= e^{\theta x/2} - \frac{4}{\sigma}\cdot \phi(\sigma/2) \tag{2.7}\\ \...
Quasar's user avatar
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Validating an option-implied risk-neutral distribution by integrating it twice and comparing the resulting "prices" with the original ones

From Breeden-Litzenberger, we know that the second derivative of a European call option's price with respect to the strike price is equal to the risk-neutral probability density function of the ...
v.y.'s user avatar
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1 vote
0 answers
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Finite difference methods for an Asian call with boundary conditions

I have a question please. I have to find the price of a Asian call using a finite diffenrece method. Here the article, if u want to look it up, it's page 2-4: "https://www.researchgate.net/...
Raphael Morel's user avatar
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1 answer
172 views

How to calibrate a volatility surface using SSVI with market data?

Context I'm a beginner quant and I'm trying to calibrate an vol surface using SPX Implied Vol data. The model is from Jim Gatheral and Antoine Jacquier's paper https://www.tandfonline.com/doi/full/10....
khubquant's user avatar
0 votes
1 answer
259 views

Verifying my understanding of replicating portfolio, hedging and option pricing

Under risk neutral measure, we use replicating portfolio to mimic the value of derivative (for example European options). Many literatures use the word "hedging" to describe the replicating ...
TJT's user avatar
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1 answer
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week-over-week impacts on IV of of options with close to before/after EOY expirations

Tomorrow is the last trading day of 2023. Compared to last week, I noticed that $SPY ATM or close-to ATM options for the end of month/quarter (Dec-29) exp experienced a spike in IV since yesterday, ...
VolatiCity's user avatar
0 votes
0 answers
71 views

Potential Future Exposure for vanilla swap

I need to calculate the PFE for vanilla swap. I wonder if it makes sense to simulate the MC scenarios with a 1-factor Hull white model. In my opinion, this model only allows parallel curve ...
SIMO's user avatar
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2 votes
1 answer
227 views

Why does the risk-free rate implied by put-call parity vary with strike prices?

Suppose I do the following: buy one lot of some underlying stock currently trading at price $S$, write a call with strike price $K$, earning some premium $C$, and buy a put with the same strike $K$, ...
Jérémie Koenig's user avatar
0 votes
1 answer
95 views

Understanding American option payoff at T+0

The above picture shows the payoff at expiry(in gold) and at current time T+0(in blue) for a bull call spread. I am trying to understand American options and to know if it has any significant ...
FawaMop's user avatar
  • 15
1 vote
0 answers
60 views

Shout option payoff replication

I have not seen much talk about exotic options, and if they are actually traded. Is it possible to replicate the payoff of a ‘Shout option’ using standard European/American call and put options?
FawaMop's user avatar
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1 vote
1 answer
320 views

Hedging exotic options

How can exotic and other path dependent, such as asian options be hedged? For example in the case of an asian option, what is the replicating portfolio: what instruments to keep in it and “how much”? ...
Kapes Mate's user avatar
3 votes
1 answer
181 views

smile dynamics IV appendix 4

I am having difficulty in recovering some result in smile dynamics of Bergomi https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1520443, the paper gives $(1-3\alpha x +(6\alpha^2 - \frac{5}{2}\beta)...
opsle's user avatar
  • 33
1 vote
1 answer
155 views

Connection between the $\sigma$ parameters of the spot price and the forward price

It is well known, that under the Black-Scholes framework: $$F\left(t,T\right)=\exp\left(r\left(T-t\right)\right)S\left(t\right),$$ where $S\left(t\right)$ is the spot price of an asset at time $t$, $F\...
Kapes Mate's user avatar
0 votes
1 answer
151 views

The metric to evaluate the efficiency of ANN based option pricing over mathematical option pricing models

The stock exchanges provide the data of option prices using theoretical formulations such as Black-Scholes formula. The dataset necessary for training an artificial neural network (ANN) to address ...
Messi Lio's user avatar
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0 votes
1 answer
110 views

Average time it takes to test a strike?

My question can be confusing so it’s better I explain it with an example. Let’s say I sell a strangle. That is with call at +27 delta and put at -27 delta. With 30 days to expiration. Is it possible ...
FawaMop's user avatar
  • 15
2 votes
2 answers
154 views

Price Option B Knowing The Price of a Similar Option A

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 ...
Kai's user avatar
  • 123
0 votes
1 answer
162 views

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 ...
Ismael2829's user avatar
0 votes
1 answer
134 views

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 ...
Maurizio Marinaro's user avatar
0 votes
3 answers
146 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 ...
gmarais's user avatar
  • 121
1 vote
3 answers
550 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-...
lambda111's user avatar
1 vote
1 answer
153 views

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 $...
MrLCh's user avatar
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0 votes
1 answer
236 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 ...
pierrot's user avatar
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2 votes
0 answers
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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 ...
pierrot's user avatar
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0 votes
0 answers
91 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, $L$ ...
humanoid's user avatar
0 votes
0 answers
137 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 $dW_{1t}dW_{2t}=\rho dt$....
Mr. Ivan's user avatar
0 votes
1 answer
153 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+...
Summerday's user avatar
  • 105
0 votes
1 answer
171 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?
FawaMop's user avatar
1 vote
0 answers
389 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 ...
Zac Likes Vol's user avatar
0 votes
0 answers
48 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-...
THATS MY QUANT MY QUANTITATIVE's user avatar
0 votes
0 answers
92 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, ...
SupSquark's user avatar
0 votes
0 answers
73 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 ...
aoliv's user avatar
  • 1
0 votes
0 answers
54 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. ...
NX37B's user avatar
  • 101
1 vote
1 answer
267 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 ...
Peaceful's user avatar
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0 votes
0 answers
48 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 ...
Dsp guy sam's user avatar

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