Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
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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 ...
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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 ...
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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 ...
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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 $t$ ...
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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 ...
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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 ...
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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 ...
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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.
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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
...
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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 $D$):
$$C^E_D(S_t,t,K,T)=e^{-D(T-t)...
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To estimate the parameters when only the characteristic function is known to us
Recently I was working with a process named Variance Gamma with Stochastic Arrival (VGSA) and trying to fit this process on a given data.
To obtain VGSA, as explained in Carr et al. [2001], we take ...
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The partial derivative of a call option with respect to $t$ [closed]
In Black-Scholes related computations, why do we not treat the stock price $S$ as a function of $t$ when taking partial derivatives with respect to $t$? For example, if
$$c(t,T)=SN(d_1)-Ke^{-r(T-t)}N(...
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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 ...
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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?
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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 ...
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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 ...
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Is it possible to reverse calculate greek, if I have the option price? [duplicate]
I purchased ES option OHLCV (open, high, low, close, volume) hourly data from Databento.
But it does not have the Greeks. I just wanted to calculate the delta to backtest a strategy.
If the "...
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How to calculate sigma in order to calculate delta? [closed]
I am calculating option delta using py_vollib.black_scholes
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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 ...
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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 ...
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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 ...
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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, "...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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}\\
\...
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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 ...
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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/...
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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....
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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 ...
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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, ...
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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 ...
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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 $K$, ...
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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 ...
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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?
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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”?
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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)...
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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\...
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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 ...
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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 ...
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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 ...
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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 ...