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Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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3 votes
1 answer
5k views

SVI model and Greeks calculation

The option pricing model I am referring to is this one: Arbitrage-free SVI volatility surfaces I calibrated that model by using a set of European options, now I have a set of 5 parameters per ...
0 votes
2 answers
72 views

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 ...
0 votes
1 answer
104 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 ...
1 vote
0 answers
33 views

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 ...
0 votes
0 answers
39 views

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 ...
0 votes
1 answer
103 views

Reconstructing the CRR model knowing put and call prices

In an arbitrage-free single-period CRR model, the following options on a share are offered: [They are all European] (i) Call option at strike price $100$, price: $C_{0,1}=7.44$ (ii) Call option at ...
0 votes
0 answers
24 views

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 ...
0 votes
0 answers
30 views

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 ...
-1 votes
2 answers
64 views

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 ...
1 vote
1 answer
300 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”? ...
0 votes
1 answer
97 views

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 ...
0 votes
1 answer
70 views

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 ...
0 votes
0 answers
53 views

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<...
-1 votes
1 answer
66 views

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 ...
1 vote
1 answer
191 views

GARCH process simulation in R

I'm trying to learn how to simulate the GARCH(1,1) for option pricing using Monte Carlo. I need to learn how to code the equations for the stock log returns and the variance process. I'm trying to ...
2 votes
1 answer
114 views

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 ...
3 votes
1 answer
2k views

Quantlib: day-by-day evaluation of option value

I'm using Quantlib in Python to price an FX option. I'm comparing the result to Bloomberg, to make sure the code is working correct. I want to calculate the P&L of a certain option trading ...
0 votes
1 answer
107 views

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 ...
0 votes
0 answers
27 views

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 ...
0 votes
1 answer
154 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....
2 votes
1 answer
385 views

How to understand broken wing butterfly option strategies?

I feel very confused about the greeks analysis for the broken wing butterfly strategy. Let's say for the stock ABC, we enter into a such strategy: we long a put option with strike $k_1$ and another ...
0 votes
1 answer
138 views

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) ...
11 votes
4 answers
8k views

How does an option's time value depend on moneyness?

How does an option's time value (also known as extrinsic or instrumental value) depend on how far it is in the money or out of the money? In other words, how does the time value change as the ...
0 votes
1 answer
62 views

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 ...
1 vote
1 answer
110 views

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 ...
0 votes
1 answer
128 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 ...
0 votes
1 answer
82 views

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 ...
0 votes
1 answer
89 views

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}_{\...
6 votes
2 answers
2k views

Option Price vs. Implied Volatility

I was doing an exercise on investigating the relationship between European Call option price and its volatility. I was asked to compute $\frac{\partial^2C}{\partial \sigma^2}$ and find out the domain ...
0 votes
0 answers
61 views

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 ...
0 votes
0 answers
38 views

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 ...
0 votes
0 answers
78 views

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 ...
3 votes
1 answer
94 views

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 ...
0 votes
1 answer
235 views

Convergence in the CRR model

Under certain conditions, the option price of the CRR (Cox-Ross-Rubinstein) Binomial model converges to the Black-Scholes price as the maximal step size of the partition converges to zero (i.e. a ...
5 votes
2 answers
642 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....
6 votes
1 answer
479 views

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 ...
0 votes
2 answers
116 views

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 ...
11 votes
2 answers
886 views

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: &...
0 votes
1 answer
121 views

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 ...
4 votes
1 answer
77 views

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 ...
2 votes
1 answer
261 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
0 answers
94 views

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 ...
0 votes
0 answers
27 views

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. ...
0 votes
1 answer
153 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 ...
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 ...
1 vote
1 answer
101 views

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 ...
0 votes
1 answer
72 views

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 $t$ ...
0 votes
1 answer
156 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 ...
0 votes
1 answer
69 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 ...
1 vote
0 answers
75 views

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 ...

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