Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
1,778
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Heston Calibration - how far OTM can an option be before it's not considered ATM anymore?
I have been doing reading and supposedly implied volatility of ATM options with 1-2 week expiries are reasonable vols to use as your $V_0$ when calibrating a Heston model.
Firstly, why would it be ...
2
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0
answers
99
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Volatility Time and Interest Rate Time
In Sheldon Natenberg's book "Option Volatiliy & Pricing (2nd)", he mentioned that (on page 65), only trading days (roughly 252 in a year) are counted when computing vol time and all ...
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1
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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 ...
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0
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1
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Difference Between Option market price and Theoretical price? [closed]
So I am working on strategies that depends on the difference between Actual market price of option and price derived using black and scholes model.
For eg: Spot 19000 , strike 19200 . It is OTM call ...
2
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1
answer
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Option Pricing for Illiquid case
I am currently studying crypto options trading and have observed that there is often a lack of liquidity for options (such as BTC Options) on various exchanges, including Binance. In many cases, there ...
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Practical consideration for the calibration of an option pricing model
Let us say that I want to calibrate for example the Heston model to some observed prices of European call options, and that I will use some different strikes and some different maturities to do the ...
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0
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asian geometric option valuation-- unable to get monte carlo simulation to converge to analytic value
I'm trying to price asian put options in which the averaging window begins immediately (T=0). currently, I'm trying to match up geometric averaging between my Monte Carlo simulations and my attempt at ...
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Best Method (Or Just a Good Method) of Predicting Intraday Volatility in Real Time?
I apologize if this is a stupid question, I'm a complete neophyte in academic finance but I am trying to learn.
I am trying to create an estimate of how likely indexes are to rise/fall by x% by the ...
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2
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QuantLib Python: How to print each caplet/floorlet value, intrinsic value and time value at each fixing date?
I have the following code to price a floor (can also be used for cap), and have been computing the payoff myself, but I think QL can already do this. Since the cashflows I print out aren't correct as ...
4
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2
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Can the risk neutral pdf derived from Breeden-Litzenberger Method be used to calculate vega and theta?
I have been researching volatility smoothing techniques and risk-neutral pdf.
I noticed one interesting post in
Does the risk neutral pdf that is derived using Litzenberger-Breeden Method correspond ...
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State-of-the-art grid construction techniques
I am wondering what the state-of-the-art regarding grid definition and construction, for solving PDEs using finite differences. I know some techniques are described in Duffy's Finite difference ...
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Accounting of a stock put option for Monthly % Changes
am looking to backtest a strategy of systemic put buying on an equity index (e.g SPX Index) so say a strategy of buying 1Y 90% SPX Puts rolled 1 day prior to expiry.
As opposed to only calculating the ...
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Option Payoff in Different Currencies
In the stackexchange answer Change of numeraire in options with currency exchange features
Pratically speaking, what this expresses is that these two things are the same:
Converting the payoff (which ...
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Leveraging Computational Techniques for Real-Life Option Pricing Models and Transforming Research into Utilitarian Products for Society [closed]
As a student specializing in computational finance, my passion lies in exploring the practical applications of advanced computational techniques in option pricing models for real-world scenarios. I ...
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Risk Neutral Pricing Exercise
I have the following exercise: A financial security pays off a dollar amount of $S_T^2$. Using Ito`s Lemma, what is the price today $V_t$ of this security? (S follows a Geometric Brownian Motion $dS = ...
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Conventions and Modeling of CDS Options
I am curious about the current standard conventions and modeling techniques in the CDS options market. I would be glad if someone could elaborate on the following topics:
State of the art of index ...
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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 ...
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Pricing European Call Closed Form Spread Options in Python
I am currently trying to correctly price European Call Closed Form Spread Options using Python. The main problem I am currently running into is that I have nothing to compare the option price so that ...
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1
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Different volatility convention
In listed option's world, sometimes I see someone put different vols interchargablly, e.g.
6.7% Vol or 171 abpv or 11 dbpv
may anyone elaborate each jargon in some detail, and how and when should they ...
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When is gamma and theta in the same direction?
So, I am reading Natenberg and it says that during expiration(close to expiration), the deep in the money options will have Gamma and Theta in the same direction. This was a bit counter intuitive to ...
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Risk-neutral density versus put-call skew and open interest
I've been experimenting with the Breeden-Litzenberger formula in Python based on some code obtained here:
https://github.com/robertmartin8/pValuation/blob/master/ProbabilisticValuation/...
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Replication of a payoff with vanilla products
A lot of research has been done in the direction of replication techniques, and most of them consider the max function. I was wondering if we have an interest rate benchmark $R$, a cap $C$, a floor $F$...
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Collateral rate vs. funding rate vs. repo rate in derivatives pricing post-GFC
I am reading Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing by V. Piterbarg.
Now I have a question about the relation of the different funding rates in the paper.
$r_C$ is ...
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Pure jump process in Duffie, Pan and Singleton's paper
In page 1349 or Section 2.1 of "Duffie, D., Pan, J., & Singleton, K. (2000). Transform Analysis and Asset Pricing for Affine Jump-Diffusions. Econometrica, 68(6), 1343-1376" the pure ...
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Can you trade options with market scoring rules?
In a double-auction market, buyers and sellers are always balanced in number -- a traditional market-maker in such markets doesn't really hold any assets/take any position long-term.
However, with a ...
2
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Is homogeneity preserved under change of measure?
In a paper, Joshi proves that the call (or put) price function is homogeneous of degree 1 if the density of the terminal stock price is a function of $S_T/S_t$. In the paper I think Joshi is silently ...
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Asymptotic behavior of implied volatility at probability mass [closed]
For sake of simplicity, let us suppose that interest rate is zero, stock price is 1, and time to expiry is 1. I am interested in implied volatility that gives the following put price.
$$P(k, \sigma(k))...
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Black-Scholes implied volatility using a GARCH model
Why I'm not getting the same Black-Scholes implied volatility values as the ones given in the paper "Asset pricing with second-order Esscher transforms" (2012) by Monfort and Pegoraro?
The ...
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API for current option quotes [duplicate]
I'm working on coding up some stuff for automated trading. Mostly just proof-of-concept type of stuff. I have found that I can get free stock quotes through the dxfeed REST API, but I also need ...
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Question about proving the existence of an arbitrage opportunity
I am having a hard time understanding the reasoning behind a statement in the proof of the following lemma from page 14 (228) of the paper "Martingales and stochastic integrals in the theory of ...
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How to price a derivative security in a trinomial asset pricing model
I am reading the first two chapters of Shreve's book "Stochastic Calculus for finance 1". The author discusses the question of how to price a derivative security assuming a binomial asset ...
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Can the PDE of Black and Scholes really be derived from the CAPM?
Black and Scholes (1973) argue that their option pricing formula can directly be derived from the CAPM. Apparently, this was the original approach through which Fischer Black derived the PDE, although ...
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How to derive the optimal option structure given investor views, i.e. is it optimal to buy a call option, a risk reversal or a butterfly
Optimizing a position typically requires two things:
An assumption about how prices will behave in the future
An objective function to maximize/minimize
For certain cases in finance, we have closed-...
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Monte-Carlo method for multi-asset pricing
As I was working on this paper https://hal.science/hal-00319947/document by Emmanuel Gobet, I came across this paragraph that says to price a barrier option on (for example) two correlated assets, you ...
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Foreign equity call struck in domestic currency
I'm trying to get a solution for the foreign equity call struck in domestic currency, where the foreign equity in domestic currency is defined as $S=S^fX^\phi$ with $0<\phi<1$, instead of the ...
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The little Heston Trap in DPS representation
I was wondering if the representation by Duffie, Pan, and Singleton (2000) is already accounting for the little Heston trap. DPS represent their 'general' discounted characteristic function as:
$$
\...
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Relationship between gamma and theta
I have read somewhere the following statements, which I have observed to be true most of the time. I want to know how accurate they are mathematically, and how to prove them?
$\Gamma > 0$ is a ...
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Three mathematical mistakes in Black-Scholes-Merton option pricing?
In this preprint on arXiv (a revised version of the one discussed in a post here) we show that there are three mathematical mistakes in the option pricing framework of Black, Scholes and Merton. As a ...
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Conditions for market completeness
We know that a market is called complete if it is possible to replicate any future payoff trading in its securities. Is there an exhaustive list of requirements that when satisfied imply market ...
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LSMC for Out of The Money paths
In the Longstaff & Schawartz article they condition on using In-The-Money (ITM) paths only for the regression. The reason for this is to obtain more accurate results and also reduce the ...
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Using CAPM to find the price of an option
I was reading a textbook about finding the price of an option on a one-period binomial model.
The textbook way of doing it is to replicate the option with cash and stock for $t=T$, and then calculate ...
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Finding upper bound for portfolio made from European call / put options
I tried finding upper bounds for each component in terms of E_1 using the put call parity but couldn’t get the correct answer.
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Dynamics of independent Geometric Brownian Motions under risk-neutral measure Q
Suppose I have two Geometric Brownian motions and a bank account:
$$dB_t=rB_tdt$$
$$
dS=S(\alpha dt + \sigma dW_t)
$$
$$
dY = Y(\beta dt + \delta dV_t)
$$
Where $dW_t$ and $dV_t$ are independent ...
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Is there a general approach to predicting future (vanilla) option prices in practice?
I realize that this question may be verging on asking for the proprietary/"secret", so if suggestion of a general approach that doesn't divulge details isn't really possible, I understand.
...
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Effect of number of monitoring points on Asian Option Price
I want to understand conceptually the expected effect of the number of monitoring points used during the average calculation on Asian options pricing and the reason of such effect.
Asian Options ...
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Formula 1.2 in book "Volatility Trading" by Euan Sinclair
I am reading "Volatility Trading" by Euan Sinclair. In the derivation of BSM process in Chapter 1, formula 1.2 confused me.
It means that the value change of a hedged call position (1 Call $...
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Heston Riccati equation
Let
$$
\begin{align*}
dY_{t} &= \left(r - \frac{1}{2} V_{t}\right) dt + \sqrt{V_{t}}dW_{t}\\
dV_{t} &= \kappa(\theta - V_{t}) dt + \rho \sigma \sqrt{V_{t}}dW_{t} + \sigma\sqrt{1-\rho^{2}}\sqrt{...
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Distribution of discrete Geometric average and Stock Price
If we have $$S_t = S_0 e^{(r-\frac{1}{2} \sigma ^2) +\sigma W_t}$$ and a discrete geometric average of stock prices $$G_n = (\prod_{i=1}^{n} S_{t_i})^{\frac{1}{n}} $$ where the monitoring points are ...
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Attributing change in option prices to greek components
A noob question. I'm trying to get my head wrapped around this but getting lost, please guide.
From the entry and exit prices of an European option, how do I attribute the P&L to various greeks (...
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