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Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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Why would you take a Loan when trying to Illustrate a Riskless Hedge?

I'm reading an article trying to derive option pricing with a simple approach, but I got stuck. In the second paragraph of this article (Name – Options Pricing: A Simplified Approach), which takes ...
Telefondemonen_se's user avatar
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Early exercise with multiple dividends

I am wondering how early exercise conditions work on multiple dividends. Say a stock pays 4 dividends in a year. We are 1 day before the first ex-div date and long an ITM Call and ITM put in an expiry ...
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Arbitrage between one touch option and vanilla option

I recently came across this question, which is if you have a one touch option which the market has priced in X% of touching the barrier, and a vanilla call option on the same underlying and maturity ...
monte-carlo-pricer's user avatar
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Approximation of an Autocall (trigger 100%) with ATM options prices

thank you very much for trying to answer this question, and I hope it will be helpful to everyone in my situation. I am preparing for an interview, and I've come across these three questions on the ...
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Option pricing model adjustments in practice

I’m trying to understand significant differences in theoretical options pricing data that I‘m seeing. I’m new to this, so I suspect I’m missing something obvious. Taking a fixed set of inputs 1, when ...
Sam C's user avatar
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Proof of the value of an option using hedging and no-arbitrage [ Paul Wilmott Chapter 3.12.2]

I encounter a difficulty in understanding the proof of finding the value of an option. Before going into the proof, let's talk above the assumptions and parameters of the model. Assume that we know ...
Ricky Pang's user avatar
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Intuition behind short 1/2 stock in option value - Paul Wilmott Quant Finance Chapter 3.3

I don't get the intuition behind the construction of long option + short 1/2 stock portfolio for finding the value of an option using binomial model. In Paul Wilmott ...
Ricky Pang's user avatar
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Pricing a custom option in terms of simpler instruments

I have the following custom European Option $F$ on the underlying $S$ whose pay-off at expiry $T$ follows: $$ F(T) = \min{[B, \max{[K_1-S(T), S(T)-K_2,0]}]} $$ where $B$ is a cash position and $0<...
Sid's user avatar
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Up and Down Multiplicative Factors of the Binomial Option Pricing Model

When computing these factors, according to some sources, $u=e^{r\Delta t+\sigma \sqrt{\Delta t}}$, where $r$ is the risk-free interest rate, $T$ is the time for maturity, and $\sigma$ is the ...
Bumblebee's user avatar
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How to price a buffet or, how to price a subscription? [closed]

I've been thinking about a problem that may not be so specific lately. How do we price a buffet, or how do we price a subscription service? In more detail, let's assume that we are a cosmetics ...
Allonsy Jia's user avatar
2 votes
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Preferred Option pricing model [closed]

I am at Uni studying mathematical finance and wanted to know which is most preferred /widely used model by Finance Industry Practitioners from the list below. Fourier Transform for option pricing ...
dijoney J's user avatar
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What are $\mu$ and $a$ in $ \mu = a + \frac{\sigma^2}{2} $

Considering GBM: \begin{equation} S(t_i) = S_0 \exp(a \cdot t_i + \sigma \cdot W(t_i)) = S_0 \exp\left((\mu - \frac{\sigma^2}{2}) \cdot t_i + \sigma \cdot W(t_i)\right) \end{equation} I am interested ...
Marlon Brando's user avatar
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option pricing under perpetual features long and short funding rate

We have perpetual futures market and we want to use it for hedging our option. On perpetual futures you pay long funding fee, if you go long or short funding fee if you go short. (The funding fee can ...
lukas kiss's user avatar
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Confusion about how price of a contingent claim at time 1 could give arbitrage

I have been reading the book Tomas Bjork's Arbitrage Theory in Continuous Time and could not understand how there could be arbitrage if the price of a contingent claim is not $X$. To give some ...
KMR's user avatar
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Pricing European Options with Monte Carlo

Given the following code (S0 = Initial Share Price, r= (risk-free) interest rate, K=Strike, Sigma= Standard Deviation, T=years, nExp=Number of Experiments) ...
Marlon Brando's user avatar
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How to arbitrage options prices against prediction markets?

Suppose we have both put/call European-style options market and price prediction market on same underlying asset and same expiration date. How can one arbitrage one against the other? It seems that ...
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Barrier Puts Pricing (down-and-in put)

I am trying to price the down-and-in put option with European Style (when barrier level < strike price) by using Black Scholes Option Pricing model. but after checking the formula several times, I ...
Wannapat P.'s user avatar
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How to access the Black Sholes Formula through the Distributive Law?

Recently I read a comment on how to interpret the Black Sholes Formula and more specifically how to wrap your head around the d1/d2. Although there were many good comments, this one stood out when one ...
Telefondemonen_se's user avatar
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Why do ATM options intuitively have higher Time Value (Extrinsic Value) than Out- and In-The-Money options?

I'm trying to get some intuition concerning the Black Sholes Formula and in doing so I've come across these graphs: Trying to understand the intrinsic value relationship with Options Value was ...
Telefondemonen_se's user avatar
11 votes
2 answers
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Why are Black-Scholes derived greeks used for risk management when alternatives exist?

To my understanding, it is still quite common for market makers of vanilla options to use Black-Scholes greeks. My concern with this is best expressed by Pat Hagan in the original SABR model paper: &...
mrdrralph's user avatar
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Difference between replicating portfolio and option price

Hello Quant Stack Exchange community, I've been working on a discrete-time model for option pricing, where I calculate the replicating portfolio using the model and compare it with the real option ...
Quant's user avatar
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If an option is undervalued, how does shorting a portfolio generate profit?

I am reading Hull's Options book. He introduces a one-step binomial model and a no-arbitrage argument, using the example shown in the picture below: Consider a portfolio consisting of a long ...
user546106's user avatar
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What are the downsides of using Kim's integral equation (1990) to determine the exercise boundary of an American option?

I'm new to the industry and trying to wrap my head around American options pricing. The integral equation(1) from Kim (1990) doesn't seem to make any strong assumptions, and approximating the integral ...
Eashan Gandotra's user avatar
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path dependency and dollar gamma

On a previous question on this website, a user derived the following PnL of a delta-hedged option: $$P\&L_{[0,T]} = \int_0^T \frac{1}{2} \underbrace{\Gamma(t,S_t,\sigma^2_{t,\text{impl.}})S_t^2}_{\...
snoreBore's user avatar
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Real options: discount rate for the value of the underlying security

This is an example inspired by Chapter 3, sub-chapter "Combining decision trees with real options(DTRO)", sub-sub-chapter "Case 4 Part Two", of Boer, F.P., 2004. Technology ...
robertspierre's user avatar
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Black scholes, issues inferring T(time to expiry) andS (underlying price)) from wrds SPX dataset

I'm working on a project with the SPX option data from wrds. This data doesn't provide the underlying price at the time of the observation, or the time to expiry at the time of the observation. ...
steve_nash's user avatar
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1 answer
146 views

Most Accurate Method for Pricing crypto Options

I'm currently studying financial derivatives and I've become particularly interested in cryptocurrency options, specifically Bitcoin. Given the unique characteristics of Bitcoin and other ...
Maria Torres's user avatar
1 vote
1 answer
98 views

Deep calibration in the Heston Model

I am doing my master thesis on deep calibration in the Heston Model, and after reading a few academic paper (eg. Horvath et al. 2019) on the subject I understand pretty well the procedure and the ...
sxminho's user avatar
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How should I go about computing the 30-day model free implied volatility (MFIV) daily?

As the title suggests, how can I calculate the MFIV daily (for a market index)? My MFIV follows the procedure described in DeMiguel et al. (2013) Improving Portfolio Selection Using Option-Implied ...
KaiSqDist's user avatar
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Mark Joshi, The concepts and practice of mathematical finance exercise 3.6

This is an exercise from Mark Joshi's book (exercise 3.6): "A stock is worth 100. Each month its value increases or decreases by precisely 10. The riskless bond is worth $e^{r t}$ at time $t$ ...
salim's user avatar
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1 vote
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Does it make sense to use Black Scholes greeks to attribute P/L given the Black Scholes assumptions don't hold?

I've seen some takes from experts in the industry (Benn Eifert for example) who say that we should treat Black Scholes as a translation mechanism for putting price into a more workable form (IV). They ...
mrdrralph's user avatar
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FX portfolio MV estimation for undelying Spot move

In the context of a project involving FX derivatives, I am faced with the challenge of estimating the change in the market value of my portfolio in response to a change in the underlying spot. The ...
AIEA's user avatar
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3 votes
1 answer
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Benth: Risk-neutral measure in incomplete markets

I am currently working on Benth and Benth "THE VOLATILITY OF TEMPERATURE AND PRICING OF WEATHER DERIVATIVES" and i am stuck at following paragraph at page 10, which is about risk-neutral ...
Valentin's user avatar
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0 answers
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Where to get Historical Options Data [duplicate]

Where can I find the historical Options Data of Bank nifty? By historical I mean more than 1 year.
Aniket Surve's user avatar
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Improvement in lower bound of American call with discrete dividends

Question Suppose a stock pays 2 discrete dividends $d_1, d_2$ at times $t_1, t_2$ respectively, where $ t < t_1 < t_2 < T.$ Assume the risk-free rate, $r$, is a positive constant. Given that ...
Hmmmmm's user avatar
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1 vote
1 answer
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Prove from Black-Scholes that value of a European call option on an asset that pays continuous dividends less than a call without dividends

Black-Scholes gives us the following formulae for the prices of European calls on an underlying that does or doesn't pay continuous constant dividends (of proportion $D$): $$C^E_D(S_t,t,K,T)=e^{-D(T-t)...
hegash's user avatar
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4 votes
1 answer
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To estimate the parameters when only the characteristic function is known to us

Recently I was working with a process named Variance Gamma with Stochastic Arrival (VGSA) and trying to fit this process on a given data. To obtain VGSA, as explained in Carr et al. [2001], we take ...
Starlord22's user avatar
1 vote
1 answer
171 views

The partial derivative of a call option with respect to $t$ [closed]

In Black-Scholes related computations, why do we not treat the stock price $S$ as a function of $t$ when taking partial derivatives with respect to $t$? For example, if $$c(t,T)=SN(d_1)-Ke^{-r(T-t)}N(...
user81883's user avatar
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4 votes
0 answers
96 views

How is option pricing related to the correlation between implied volatlity and the underlying?

The correlation between the index returns (e.g SPX) and its changes in option-impled volatility (e.g. VIX), is strong, stable and negative (the implied volatility feedback effect). To me at least, it ...
Mats Lind's user avatar
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Can someone please help me answer this question about Black-Scholes model? (risk-neutral & true probability of the call option) [closed]

I don't even know where to get started with this question...can someone please help me? How do I answer it?
Jolie's user avatar
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Why is my Risk Neutral Density recovery failing?

I'm working on a project to recover a known Risk Neutral Density from option prices, using the Breeden-Litzenberger formula (assuming a continuum of option_price(strike_price), the second derivative ...
v.y.'s user avatar
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0 votes
0 answers
97 views

Positive Theta for an At The Money option (with real data)

Ive been doing some work on looking at historical options prices on a stock index using real data, and I came across an odd example that I cant really get my head around. I am aware that for extreme ...
Arron's user avatar
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-2 votes
2 answers
185 views

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 votes
0 answers
155 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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0 answers
36 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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0 votes
1 answer
152 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
151 views

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 vote
1 answer
113 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
233 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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