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Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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FX Option - Conversion of Premium Currency From Domestic to Foreign Currency

I’m trying to price a put FX option on USD/TRY exchange rate. How can I calculate the premium in foreign currency (USD). Can I directly divide the domestic premium by the spot rate? The premium for ...
jack's user avatar
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resolve the DUPIRE Forward PDE

I want to implement the "Dupire forward PDE". I will use this PDE to calibrate a parametric local volatility model. Could you recommend an article or link that explains concretely how I can ...
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Simple arbitrage pricing of bond option

This is Tuckman fixed income security textbook. The text here is trying to price a 990 six month call on a six month zero bond. When we replicate the portfolio, where is the F_.5 coming from? My ...
Austin Jin's user avatar
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Vol Shift by Term over Time

Below is a plot of AAPL vol vs. Strike for October and November, last market close vs 3 weeks prior. The plot shows that both curves shifted up by an approximately constant amount with the October ...
PentiumPro200's user avatar
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Potential arbitrage opportunity or fallacy?

Suppose we have two European options with the same expiration: a call priced at $c$ with strike price $K_1$ and a put priced at $p$ with $K_2 (>K_1)$. Further, suppose the zero-points of the two ...
Ambitious-Walk3171's user avatar
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Volatility in simulated paths different to monte carlo parameters

I am trying to convince myself that I have set up my monte carlo simulation correctly by looking at the results and trying to get them to agree with the model parameters. Please help me understand ...
Bartosz Wozniak's user avatar
2 votes
1 answer
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FX risk reversal approximation

i see this risk reversal approximation in Uwe Wystup's https://www.mathfinance.com/wp-content/uploads/2020/09/wystup_vannavolga_eqf.pdf in which the approximation of a risk reversal is given by: vega ...
Mikey's user avatar
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What pricing curve to use for different instruments?

When pricing derivatives, their price depends on some yield curve, which is used to discount future cash flows. But there are many yield curves, dependent on what they're bootstrapped from. There's ...
Jaood's user avatar
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Price of options when exercise date doesn't match nodes of BDT Tree

I think I'm missing something obvious here, but here I go. I'm studying pricing of bonds with embedded options using Black Derman Toy. I understand tree construction and its application for simple ...
PLE's user avatar
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Find a formula for the price of a derivative paying $\max(S_T^2-K,0)$ [duplicate]

Develop a formula for the price of a derivative paying $$\max(S_T^2-K,0)$$ in the Black Scholes model. What I tried: \begin{align*} e^{-rT}\mathbb{E}^\mathbb{Q^0}[\max\{S_T^2-KS_T,0\}] = e^{-rT}\left(...
DivertingPie's user avatar
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Changing parameterization in Dupire's Formula

In chapter 2 of Bergomi's book on stochastic volatility, we have dupire's formula given as $$\sigma(S, t)^2 = \left|\frac{\frac{\partial C}{\partial T} + (r-q)K\frac{\partial C}{\partial K} + qC}{\...
I_cosine_this's user avatar
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Understanding assumption in Delta hedging P&L from Bergomi Chapter 1

In Chapter 1 of Bergomi's Stochastic Volatility modelling book there is a derivation of the delta hedging P&L to get a black-scholes like formula. The derivation in the multi asset case goes ...
I_cosine_this's user avatar
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Valuation of forward-starting call with non-zero strike

We know prices for call spread options with strike $K\neq0$ that is an option whose payoff $\varphi(S_T^1,S_T^2)$ is given by: $$\varphi(S_T^1,S_T^2):=(S_T^1-S_T^2-K)^+$$ where $S^1,S^2$ are the ...
Daneel Olivaw's user avatar
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BOUNDARY CONDITIONS OF A SABR PDE

I am looking to solve a sabr partial differential equation numerically using finite volume method, but I don't seem to find any information about the boundary condition to apply. Below is the form of ...
Mwale Richard's user avatar
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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 ...
Arbitrageously's user avatar
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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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1 answer
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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
1 answer
180 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 ...
dijoney J's user avatar
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1 answer
117 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 ...
Marlon Brando's user avatar
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31 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 ...
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 ...
uhbif19's user avatar
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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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81 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 ...
Telefondemonen_se's user avatar
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2 answers
137 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 ...
Telefondemonen_se's user avatar
11 votes
2 answers
902 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: &...
mrdrralph's user avatar
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1 vote
1 answer
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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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1 answer
126 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 ...
user546106's user avatar
4 votes
1 answer
79 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 ...
Eashan Gandotra's user avatar
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104 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}_{\...
snoreBore's user avatar
1 vote
0 answers
95 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 ...
robertspierre's user avatar
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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. ...
steve_nash's user avatar
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1 answer
194 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
108 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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1 vote
1 answer
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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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0 votes
1 answer
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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
0 answers
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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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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
1 vote
0 answers
51 views

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 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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