Skip to main content

Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

Filter by
Sorted by
Tagged with
68 votes
9 answers
92k views

What are some useful approximations to the Black-Scholes formula?

Let the Black-Scholes formula be defined as the function $f(S, X, T, r, v)$. I'm curious about functions that are computationally simpler than the Black-Scholes that yields results that approximate $...
knorv's user avatar
  • 2,119
48 votes
9 answers
5k views

Are there any new Option pricing models?

Back in the mid 90's I used the Black-Scholes Model and the Cox-Ross-Rubenstein (Binomial) Model's to price Options. That was nearly 15 years ago and I was wondering if there are any new models being ...
Piers Myers's user avatar
47 votes
16 answers
35k views

Why Drifts are not in the Black Scholes Formula

This question has puzzled me for a while. We all know geometric brownian motions have drifts $\mu$: $dS / S = \mu dt + \sigma dW$ and different stocks have different drifts of $\mu$. Why would ...
CuriousMind's user avatar
38 votes
5 answers
22k views

How should I calculate the implied volatility of an American option in a real-time production environment?

There are many models available for calculating the implied volatility of an American option. The most popular method, employed by OptionMetrics and others, is probably the Cox-Ross-Rubinstein model. ...
Tal Fishman's user avatar
  • 13.5k
37 votes
0 answers
1k views

How to show that this weak scheme is a cubature scheme?

Weak schemes, such as Ninomiya-Victoir or Ninomiya-Ninomiya, are typically used for discretization of stochastic volatility models such as the Heston Model. Can anyone familiar with Cubature on ...
TheBridge's user avatar
  • 4,573
34 votes
3 answers
9k views

How do we use option price models (like Black-Scholes Model) to make money in practice?

In quantitative finance, we know we have a lot of option price models such as geometric Brownian motion model (Black-Scholes models), stochastic volatility model (Heston), jump diffusion models and so ...
nkhuyu's user avatar
  • 605
33 votes
11 answers
19k views

Probability of touching

For a vanilla option, I know that the probability of the option expiring in the money is simply the delta of the option... but how would I calculate the probability, without doing monte carlo, of the ...
glyphard's user avatar
  • 3,646
29 votes
0 answers
676 views

Is there a relationship between Risk Neutral Pricing framework and Nash Equilibria?

Based on the Fundamental Theorem of Asset Pricing, the risk neutral price of a contingent claim on an asset in a liquid, arbitrage free market can be determined by switching to an equivalent $Q-$ ...
Ali Fathi's user avatar
  • 421
28 votes
3 answers
16k views

Explaining 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 ...
Trajan's user avatar
  • 2,532
25 votes
6 answers
31k views

What is the implied volatility skew?

I often hear people talking about the skew of the volatility surface, model, etc... but it appears to me that there isn't a clear standard definition unanimously used by practitioners. So here is my ...
TheBridge's user avatar
  • 4,573
23 votes
3 answers
4k views

When do Finite Element method provide considerable advantage over Finite Differences for option pricing?

I'm looking for concrete examples where a Finite Element method (FEM) provides a considerable advantages (e.g. in convergence rate, accuracy, stability, etc.) over the Finite Difference method (FDM) ...
Alexey Kalmykov's user avatar
22 votes
1 answer
2k views

What is the trickiest thing to get right in Rates Quant recently (2019)?

What are the biggest challenges for Rates Quants in 2019? Most quants have been through a lot over the past years-shifting their SABR models in JPY swaptions, fixing the FVA models for negative rates, ...
NBF's user avatar
  • 1,078
21 votes
6 answers
19k views

Risk Neutral Probability

I read that an option prices is the expected value of the payout under the risk neutral probability. Intuitively why is the expectation taken with respect to risk neutral as opposed to the actual ...
Mykie's user avatar
  • 345
21 votes
4 answers
8k views

How to solve for the implied stock lending rate given equity options prices?

When market makers price options on hard-to-borrow equities, they include the cost to borrow the underlying equity that their broker is going to charge them to sell the security short to hedge. I'm ...
unclepaul84's user avatar
20 votes
8 answers
16k views

Why does implied volatility show an inverse relation with strike price when examining option chains?

When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts. As a current ...
Joseph Tanenbaum's user avatar
20 votes
3 answers
14k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
Jeffrey's user avatar
  • 203
20 votes
4 answers
6k views

From Fourier Transforms to Option Values

I am trying to understand how Fourier transforms & Characteristics functions can be used to calculate option values. However, I am having difficulty following the process that is used in several ...
sets's user avatar
  • 1,471
19 votes
3 answers
3k views

Hedging Covid-19 and other low probability high loss risks

Covid-19 and similar risks are low probability, high loss events. Does it make sense to utilize options to provide hedges for such events? For example, should one utilize long positions in deep out-...
AlRacoon's user avatar
  • 6,632
18 votes
7 answers
8k views

Formal proof for risk-neutral pricing formula

As you know, the key equation of risk neutral pricing is the following: $$\exp^{-rt} S_t = E_Q[\exp^{-rT} S_T | \mathcal{F}_t]$$ That is, discounted prices are Q-martingales. It makes real-sense ...
SRKX's user avatar
  • 11.1k
18 votes
2 answers
1k views

Duality between constant rebalanced portfolio (CRP) and corresponding derivative

One of the greatest achievements of modern option pricing theory is finding corresponding dynamical trading strategies in linear instruments with which you can replicate and by that price derivative ...
vonjd's user avatar
  • 27.5k
17 votes
5 answers
10k views

How to get greeks using Monte-Carlo for arbitrary option?

Let's assume I have an arbitrary option that I can price using Monte-Carlo simulation. What is the general approach (i.e. without relying on specific option type) to calculating the greeks in this ...
Alexey Kalmykov's user avatar
16 votes
5 answers
49k views

Bachelier model call option pricing formula

Does anybody have the Bachelier model call option pricing formula for $r > 0$? All the references I've read assume $r = 0$. I don't speak French, so I can't read Bachelier's original paper.
Galsunja's user avatar
  • 161
16 votes
8 answers
7k views

Consensus on Cauchy distribution for stock prices

What is the general consensus for using a Cauchy distribution to model stock prices? I can't find much after researching online and wonder if it has been tried and discarded. My motivation is to find ...
rwolst's user avatar
  • 337
16 votes
4 answers
8k views

How does volatility affect the price of binary options?

In theory, how should volatility affect the price of a binary option? A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now let's ...
CQM's user avatar
  • 1,862
16 votes
3 answers
7k views

How can one compute the Greeks on VIX Futures

I am guessing the short answer to this question is "use the chain rule and linearity of the derivative," but I am looking for more specific advice on how to compute the derivatives of a VIX futures ...
shabbychef's user avatar
  • 2,836
16 votes
3 answers
2k views

How to price a volatility-index option?

There exist several volatility indices, such as the CBOE Volatility Index (VIX). There are also options on such indicies. What is the best way to price a volatility-index option? Is there a simple ...
zoom's user avatar
  • 410
16 votes
1 answer
703 views

Max option leverage strike

Since options represent leveraged stock investments, at which strike $K$ does a European option provide maximum leverage? Hereby define leverage $L$ as ratio of Delta/Optionprice: $$L(K)=\frac{\...
emcor's user avatar
  • 5,795
16 votes
1 answer
2k views

How do I price OANDA box options?

How do I price OANDA box options without using their slow and machine-unfriendly user interface?: http://fxtrade.oanda.com (free demo account) sells "box options": If you already know what a box ...
user avatar
15 votes
4 answers
4k views

Methods for pricing options

I'm looking at doing some research drawing comparisons between various methods of approaching option pricing. I'm aware of the Monte Carlo simulation for option pricing, Black-Scholes, and that ...
amr's user avatar
  • 261
15 votes
3 answers
20k views

Are there comprehensive analyses of theta decay in weekly options?

Are there comprehensive analyses of how much theta a weekly options loses in a day, per day? I know what the shape of theta decay looks like, in theory, where the decay towards zero happens more ...
CQM's user avatar
  • 1,862
15 votes
2 answers
1k views

What are important model and assumption-free no-arbitrage conditions in options trading?

In the paper "Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula" (Espen Gaarder Haug, Nassim Nicholas Taleb) a couple of model-free arbitrage conditions are mentioned which limits ...
knorv's user avatar
  • 2,119
14 votes
1 answer
4k views

How do different models impact option Greeks?

If I trade an option using delta, vega, Prob OTM, etc. these are derived from a model. How do leading models impact valuations in terms of the Greeks? I suppose to form a baseline it would have to be ...
Jon's user avatar
  • 141
14 votes
3 answers
9k views

How does one go from measure P to Q(risk-neutral) when modeling an asset paying dividends?

I am really having a terrible time applying Girsanov's theorem to go from the real-world measure $P$ to the risk-neutral measure $Q$. I want to determine the payoff of a derivative based an asset ...
John Tyree's user avatar
14 votes
3 answers
2k views

Historical Volatility vs Implied Volatility Performance in Pricing Options

I consistently read on academic papers, when pricing options, using implied volatility is better than using historical volatility. Because, market is more "forward-looking" and historical data is "...
berkorbay's user avatar
  • 1,051
13 votes
4 answers
11k views

Ways of treating time in the BS formula

The Black-scholes formula typically has time as $\sqrt{T-t}$ or some such. My questions: What is the granularity of this? If we treat $t$ as the number of days, then logically on the day of expiry, ...
Dmitri Nesteruk's user avatar
13 votes
3 answers
10k views

Black-Scholes under stochastic interest rates

I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...
Egodym's user avatar
  • 698
13 votes
2 answers
4k views

What are the main flaws behind Ross Recovery Theorem?

Stephen Ross’ new paper claims that it is possible to separate risk aversions and historical probabilities if the Stochastic Discount Factor is transition independent using Perron-Frobenius Theorem. ...
fni's user avatar
  • 1,896
13 votes
2 answers
21k views

How to numerically obtain delta?

The delta in option pricing, also called the hedge ratio, is expressed as the sensitivity of the option price to the underlying price change. The analytical solution for the most common option ...
JohnAndrews's user avatar
13 votes
4 answers
538 views

How to price very short dated options?

I was wondering if there is any industry standard in pricing very short dated options, from say 6h options down to 5 minute options. My thinking is that as time to expiry gets shorter and shorter, the ...
apocalypsis's user avatar
13 votes
1 answer
668 views

Transformation of Volatility - BS

I have recently seen a paper about the Boeing approach that replaces the "normal" Stdev in the BS formula with the Stdev \begin{equation} \sigma'=\sqrt{\frac{ln(1+\frac{\sigma}{\mu})^{2}}{t}} \end{...
Corn's user avatar
  • 181
13 votes
0 answers
505 views

Jim Gatheral's ansatz

In the Ansatz section of Jim Gatheral's book Volatility Surface (page 32), he assumes $$\mathbb E[x_s|x_T]=x_T\frac{\hat w_s}{\hat w_T}$$ where $\hat w_t:=\int_0^t \hat v_s ds$ is the expected total ...
Hans's user avatar
  • 2,806
12 votes
3 answers
2k views

What tools are used to numerically solve differential equations in Quantitative Finance?

There are a lot of Quantitative Finance models (e.g. Black-Scholes) which are formulated in terms of partial differential equations. What is a standard approach in Quantitative Finance to solve these ...
Roman's user avatar
  • 529
12 votes
2 answers
7k views

Heston Model Option Price Formula

What is the formula for the vanilla option (Call/Put) price in the Heston model? I only found the bi-variate system of stochastic differential equations of Heston model but no expression for the ...
emcor's user avatar
  • 5,795
12 votes
2 answers
3k views

How to transform process to risk-neutral measure for Monte Carlo option pricing?

I am trying to price an option using the Monte Carlo method, and I have the price process simulations as an inputs. The underlying is a forward contract, so at all times the mean of the simulations is ...
airguru's user avatar
  • 693
12 votes
1 answer
327 views

How should FX options be priced when a currency is artificially capped?

The question is inspired by yesterday's (06/09/11) historic announcement by the Swiss National Bank that it would impose a ceiling on the franc of 1.20 against the euro. I would like to know if there ...
olaker's user avatar
  • 5,080
12 votes
1 answer
2k views

How to price a Swing Option?

I'm working in the commodity market and I've to price Swing Options with MATLAB, preferably with finite element. Has anyone already priced these kind of derivatives? I'm thinking about using the ...
alberto's user avatar
  • 121
11 votes
4 answers
2k views

Intuition for Stock Price Numeraire Drift

I would like to ask whether there is an intuition for the drift of price processes under the Stock numeraire. I find it intuitive that the martingale measure under the Money Market numeraire induces ...
Jan Stuller's user avatar
  • 6,178
11 votes
3 answers
1k views

How to choose a risk-neutral measure when the market is incomplete?

I am more of a probabilist than a financial mathematician. I am currently working on the features of American put options under a particular stochastic volatility model. Like most stochastic ...
Lost1's user avatar
  • 1,023
11 votes
3 answers
8k views

Option Pricing Model Calibration In Practice

I'm curious how an option pricing model like the Heston model is calibrated in practice. Here's how I imagine it happens: Let's say I have access to the most recent option prices on a given stock ...
bcf's user avatar
  • 2,828
11 votes
3 answers
2k views

Reference on Markov chain Monte Carlo method for option pricing?

I have to implement option pricing in c++ using Markov chain Monte Carlo. Is there some paper which describes this in detail so that I can learn from there and implement?
Shane Wingard's user avatar

1
2 3 4 5
37