Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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Meta-Theorem Bjork, arbitrage and completeness

In Tomas Björk's Arbitrage Theory in Continuous Time I found this Meta-Theorem: What does it mean "meta-Theorem"? That it cannot be proved and that this is only such an indication as to ...
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1answer
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How to estimate the risk-free rate when pricing options - calibration

I would like to calibrate my model to the current call option prices (with 17 different maturity times) but I don't know how to choose a risk-free rate in this case.
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Stocks with same volatility but different drifts

In the book Quant Job Interview Questions & Answers, in section 2, question 2.4 says suppose two assets in a Black-Scholes world have the same volatility but different drifts. How will the price ...
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297 views

Why does implied volatility decrease without a change in stock price?

I was lookin at some stocks and find that implied volatility changes without the stock price moving too much. What are the causes?
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Black Scholes model calibration with Python - small error in the code

Hey I write this code to calibrate Black Scholes model, but I got an error and I don't know how to correct it. Can anyone look and tell me what should I do? ...
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Kou model matlab/python code [closed]

Hey I need some code to implement the Kou model to price call option. I prefer Python but can be any other language. I am not a programmer, so I can not write it myself. Cna anyone help me?
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How to select data for model calibration

I would like to calibrate the model to the current price of an Apple stock call option. How to select data for calibration? Because for this stock there are a lot of call options with 17 different ...
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1answer
56 views

Why does the closed formula result for a Barrier option price deviate so strongly from the Monte Carlo approximation?

I am trying to price a down-and-out, leveraged Barrier option using the closed form formula of Hull (2015). When the price of the underlying asset falls and hits a certain barrier (H), the contract ...
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1answer
77 views

How to calculate dividend yield - option pricing

Hey how do you calculate the dividend rate if you want to price your stock options eg apple? Just take the dividends paid last year and divide by today's share price? This page reports 0.85% (https://...
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What put options would the Universa Tail Fund have bought?

According to this Bloomberg article, Universa was up 3,600% in March 2020, by hedging with extremely out-of-the-money puts: https://www.bloomberg.com/news/articles/2020-04-08/taleb-advised-universa-...
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Price of Call & Put Spreads as Volatility Tends to Infinity in Bachelier Model

In the standard Black Scholes model, as we take volatility to infinity, the price of call spreads goes to zero and the price of put spreads goes to the difference in strikes. I ran a simulation using ...
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Expected Option Payoff equal to 0 [closed]

How much would you sell an option whose expected payoff equals 0?
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Change of Measure for Jump Process with Drift and no Brownian motion

If on $(\Omega, \mathcal{F},\mathbb{P})$, $r>0$ is a constant and $Z_t =\sum_{i=1}^{N_t} Y_i$ where $Y_i$ are i.i.d with $E[Y_i]=L$ denotes the size of the jump and can have distributions like ...
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Why do we not use copula for forward starting options?

Why do we use copulas for spread options but do not use them to correlate random variables across time, such as in the forward starting option?
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Estimate profit/loss of short-term SPX options with only underlying price (entry/exit) and delta [closed]

If we know the underlying price (SPX index or SPY) at entry/exit of a short-term trade with SPX options, what is the best way to estimate the profit/loss of the trade? Underlying profit times delta ...
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Infinitesimal Generators and Expectation of First Hitting Time as Solution of Differential Equation

I've been learning about Linear Diffusions and how their infinitesimal generators can be used to relate expectations and deterministic differential equations. Let $X$ be an one-dimensional diffusion ...
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Confusion about replicating a call option

Assume standard Black-Scholes model, $$dS(t)=S(t)(rdt+\sigma dW(t))$$ where $\sigma$ is a constant and $W(t)$ is a Brownian motion under the risk neutral measure. A call option is replicable, so if we ...
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Why are these deep in-the-money FLEX options seemingly bought at a discount?

98% of the initial reference value is .98 x 267.88 dollars, which equals 262.52 dollars. However, the market value of each call contract they purchase is 247.42 dollars. How are they purchasing these ...
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Options when there's no VolSurf - Emerging/Frontier Markets

Context: Most emerging/frontier markets have no or very thinly traded volatility surfaces for their equity markets (single name and indices alike), furthermore, they usually have restrictions on Short-...
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How is the implied risk neutral density affected when changing numeraire?

For example i would like to price \begin{equation*} E^{Q} \left[ e^{-\int_{0}^{T}r_{s}^{cur}ds} f \left( S_{T_f}^{cur_1} \right) | \mathcal{F}_{0} \right] = B_{cur}(0,T)E^{Q^{cur}_{T}}[ f(S_{T_f}^{...
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Changing numeraire in Margrabes formula

Consider a Black Scholes market with constant coefficients, a bond and two risky assets: $$dB_{t}=r B_{t}dt \\ dS_{t}^{i}=S_{t}^{i}(b_{i}dt+\sigma_{i,1}dW_{t}^{1}+\sigma_{i,2}dW_{t}^{2})$$ where $i=1,...
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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 ...
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Hand coded algorithm for tangent algorithmic differentiation

I'm looking for a way to hand code the algorithm for the forward/tangent mode of algorithmic differentiation to calculate option Greeks with Monte Carlo simulations. The computational power is very ...
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1answer
77 views

Option data analysis

This question is regarding the following tweet: https://twitter.com/yuriymatso/status/1281730109141954561 How was the original tweeter able to know that "Someone made a ...
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1answer
68 views

What options are typically priced in practice by Monte-Carlo simulation?

More or less as the title states, for which options is the industry standard to price using Monte-Carlo simulation of the underlying, and for which of those options is this the only alternative? I ...
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1answer
40 views

Confusion about optimal choices with exotic options

With exotic options, holders usually face choices at certain times. In my understanding, the price of the option is determined by assuming the optimal choice is taken and computing the discounted ...
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Confusion about American style option

In American style exotic options, the holder is often faced with choices at certain times during the life span of the option. Following the/an optimal choice allows the user to maximize the value of ...
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52 views

How does most Forex options work? What is the most liquid or popular type of forex options?

For the "mainstream" forex options for example those (in the size of bn) posted on this site: https://www.forexlive.com/orders/!/fx-option-expiries-for-thursday-july-02-at-the-10am-ny-cut-...
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Higher moments of a straddle

Following the logic of Ben-Meir and Schiff (2012) and this question the first, second, third and fourth raw moments of a put are: Similarity, for a call it is as follows: where and ...
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Finding a PDE for an option $V(t,r(t),S(t))$

I have 2 approaches in my mind for finding a pde of an option that depends both on the short rate as well as the stock price- $V(t,r(t),S(t)$. Are these equivalent? Find a hedging portfolio by ...
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2answers
655 views

“The potential gain of a Call Option is always incorporated in the Option's price” - Why is that?

I've heard this but I don't understand why. The demonstration of this is that the Ask Price of a Call Option is always higher than the difference between the Strike Price and the price of underlying ...
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What are some alternatives to Geometric Brownian motion that can be used in the Black-Scholes? [closed]

I hear that there are many extensions to the black scholes model to make it more realistic, however, GBM does not account for volatile swings. Is there any sort of alternative approach to use instead?
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278 views

Why are interest supposed deterministic for equity?

I don't see why would rates be considered as deterministic when trying to price $\mathbb{E}^{Q} \left[ e^{-\int_{0}^{T_{f}}r_{s}ds} \left( S_{T_f} \right) | \mathcal{F}_{0} \right]$ I would like to ...
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2answers
104 views

Compute the price of a derivative which pays $\log(S_T)S_T$ in the Black Scholes world

Compute the price of a derivative which has pays $\log(S_T)S_T$, you can assume that the Black Scholes model is valid. Using the stock measure we can write the expectation as $$D(0) = S_0 \mathbb{E}...
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4answers
372 views

Find a formula for the price of a derivative paying $\max(S_T(S_T-K),0)$

Develop a formula for the price of a derivative paying $$\max(S_T(S_T-K))$$ in the Black Scholes model. Apparently the trick to this question is to compute the expectation under the stock measure. So,...
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What is the typical work-flow and skills/techniques required for someone working on Structuring Products?

Are there any Portfolio Optimization techniques (Markowitz, Prospect Theory, etc...), valuations and derivatives hedging techniques? What is a typical workflow and what should one master?
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2answers
64 views

Graph of a down-and-in barrier option

Here is a graph of Price vs Spot from Joshi's Quant Interviews book, The first line is a down-and-out barrier option and the other one is a down-and-in barrier option. The strike is 100 and the ...
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4answers
191 views

Price of Call Option with or without jumps

Suppose two assets in the Black Scholes world have the same volatility, but different drifts and that one has downward jumps at random times. How does this affect the option prices? I would have ...
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1answer
54 views

FX pricing replication

Pay in currency : cur The FX is : $FX^{cur_2/cur_1}$ European options on the FX (and itself) are quoted in currency cur 1. I'm looking for the price of \begin{equation*} \mathbb{E}^{Q} \left[ e^{-\...
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2 Equity with different currencies and different fixing dates

Given Pay in currency : cur european options on the underlying 1 (and itself) are quoted in currency 1 with fixing date 1 european options on the underlying 2 (and itself) are quoted in currency 2....
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1answer
82 views

Pricing multidimensional equity

How would you price \begin{equation*} \mathbb{E}^{Q} \left[ e^{-\int_{0}^{T}r_{s}ds} f \left( S_{T_f}^1, S_{T_f}^2 \right) | \mathcal{F}_{0} \right]\end{equation*} with $T_{f} \le T$ and $S^{1}, S^{...
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101 views

Best practices for C++ development in quantitative finance [closed]

I'm been working as a quant for the past 10 years, but have managed to avoid any significant C++ projects until now. I typically use a combination of kdb, R, and python. I've now been tasked with ...
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1answer
80 views

Implied volatility of hypothetical options market

I am attempting to create a volatility surface for a US electricity market that has a liquid futures market but nearly non-existent options market (<5 trades per month across all strikes and ...
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2answers
52 views

Value Option with Forward Volatilities

That is probably a rather simple question but I got confused and would be very thankful for help. Imagine we are in 2015 and have an option that expires in either 2016, 2017, 2018, 2019, 2020 or 2021. ...
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Convenience yield

I need to price an option on gold in some local currency. If I use the Black Scholes formula, then I need to input convenience yield for spot gold. Given generally available market data, how can I ...
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3answers
553 views

What is the Risk Neutral Measure?

What is the Risk Neutral Measure? I don't believe this has been answered on the internet well and with all the parts connecting. So: What is the risk neutral measure/pricing? Why do we need it? How ...
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1answer
177 views

Software implementation for valuation of exotic options

I am looking for some software implementation of pricing Average Price Call option (APO) mostly Python (or any other package.) Exercise style is ...
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1answer
61 views

CDS Option pricing in quantlib python

I am newbie in Python and I am trying to price a CDS Option in quantlib Python. I have the below code: ...
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2answers
139 views

How does a pricing model 'understand' the cost of hedging?

Suppose I am pricing a multi asset at the expiry payoff. Theoretically I define their joint distributions in the risk neutral measure, and price using expectation. However, how do I know that the ...
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2answers
82 views

How does high IV effect a put backspread?

I have a hard time understanding how high IV effects the amount of gamma obtained via a put backspread. Is it via the angle on the payoff or via the ratio one gets i.e number of OTMs one can buy? or ...

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