Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
218
questions
6
votes
2
answers
3k
views
Garman-Kohlhagen (Black-Scholes) Formula vs. Bloomberg OVML Calculator
I'm trying to price a European call option on USDJPY. We have that $S = 112.79, K = 112.24, \sigma = 6.887\%, r_d = 1.422\%, r_f = -0.519\%, T = 0.25$. My model, based on Black-Scholes, returns the ...
- 440
3
votes
3
answers
3k
views
FX Option pricing on Forward vs. Spot
In a GBM world with riskless domestic and foreign interest rates, what would be the correct model for a FX plain vanilla option given the statement that this option is priced on the forward? I guess ...
- 163
67
votes
9
answers
87k
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 $...
- 2,109
27
votes
3
answers
14k
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 ...
- 2,462
47
votes
16
answers
33k
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 ...
- 765
4
votes
3
answers
1k
views
Derivation of BS PDE problem using Delta hedging
I've always been confused with Delta hedging. It is well-known that for a (smooth enough) function of $(S,t)$ we have, due to Ito's lemma, that:
\begin{eqnarray*}
dC = \left(\frac{\partial C}{\partial ...
- 893
17
votes
5
answers
46k
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.
- 171
7
votes
4
answers
2k
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,...
- 2,462
12
votes
3
answers
9k
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 ...
- 678
4
votes
3
answers
2k
views
Probability of an Option maturing In-the-money vs. Volatility
How will the probability of an option ending up in the money change if the volatility of the underlying stock increases?
Intuitively, I think the answer to this is that if volatility goes up the ...
- 2,462
3
votes
1
answer
1k
views
Quantlib: day-by-day evaluation of option value
I'm using Quantlib in Python to price an FX option. I'm comparing the result to Bloomberg, to make sure the code is working correct.
I want to calculate the P&L of a certain option trading ...
- 95
20
votes
6
answers
18k
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 ...
- 335
20
votes
3
answers
13k
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, ...
- 203
9
votes
5
answers
4k
views
Estimate probability of limit order execution over a large time frame
I have a negligible amount of money (\$5000) that I would like to invest in a stock. I would like to buy the stock at some point in the next year, and get the lowest possible price.
I would like to ...
- 93
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. ...
- 13.4k
33
votes
11
answers
18k
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 ...
- 3,646
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 ...
- 141
4
votes
1
answer
3k
views
Quantlib: Greeks of FX option in Python
I'm using Quantlib in Python to price an FX option.
I'm comparing the result to Bloomberg, to make sure the code is working correct.
I also want to calculate all the Greeks, and eventually use those ...
- 95
2
votes
3
answers
5k
views
FX Delta Conventions
I'm currently reading Iain Clark's book Foreign Exchange Option Pricing and I got stuck at one sentence in the beginning of Section 3.3 that I feel is important to understand. He writes:
FX ...
- 599
1
vote
1
answer
473
views
How do trading platforms estimate options pricing P&L graphs?
Using the profit/loss calculator for equity option strategies of a trading platform, it displays estimated P&L curves for some date in the future and across the prices of the underlying with a ...
- 113
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 ...
- 963
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, ...
- 2,022
12
votes
0
answers
474
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 ...
- 2,736
10
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 ...
- 5,998
6
votes
2
answers
1k
views
Importance Sampling for pricing options with longstaff and schwartz
I have been asking this similar question before. However, I really want to be concrete and get and concrete explanation.
I have been reading the paper by Moreni and try to implement the same ...
- 427
6
votes
2
answers
2k
views
Option Price vs. Implied Volatility
I was doing an exercise on investigating the relationship between European Call option price and its volatility. I was asked to compute $\frac{\partial^2C}{\partial \sigma^2}$ and find out the domain ...
- 133
5
votes
1
answer
4k
views
Option prices in Bates SVJ model?
In this [post] discussed the European put and call price formulas under the Heston Stochastic Volatility model.
There exists an important extension of Heston model to include diffusion jumps, known ...
- 5,749
4
votes
1
answer
3k
views
Numerical example of how to calculate local vol surface from IV surface
I'm looking for an excel example (not a copy of Dupire's eqn) of how to convert an IV surface to a local vol surface. If unsuccessful I'll work through Dupire's eqn but would be helpful to look at an ...
- 219
4
votes
1
answer
414
views
Bartlett's delta gives wrong signs for calls and puts
There is a paper by Bruce Bartlett introducing a modified delta for SABR model which accounts for the correlation between forward and volatility processes. The main result of the paper is that if $dF$ ...
- 764
3
votes
1
answer
483
views
Intuition behind prices modeled by Geometric Brownian Motion
Suppose that we model a price $P_t$ to evolve per
$$\frac{dP_t}{P_t}=\mu dt+\sigma dW_t$$
for $\mu\in\mathbb{R}$ and $\sigma>0$. The unique strong solution to this diffusion is
$$P_t=P_0e^{(\mu-\...
- 155
3
votes
2
answers
445
views
Structuring and Customization
It seems complex derivatives in particular exotic options are not available at any retail broker. Can a regular retail trader get access to these instruments? Maybe through prop firms or banks? ...
user57027
3
votes
2
answers
1k
views
Put-Call relationship for Option on Forward
The forward price of a forward contract maturing at time T on an asset with price St at time t is,
$$
F=S_te^{(r-q)(T-t)}
$$
where $r$ is the risk free rate and $q$ is the continuous dividend rate ...
- 514
3
votes
2
answers
1k
views
SABR model - beta
In the SABR model, the parameter beta largely controls the back-bond behaviour of the model. How do people estimate beta?
One approach is to regress atm vol vs forward, i.e.
$$\ln(\textrm{atm vol}) = \...
- 31
2
votes
1
answer
1k
views
Probability of exercise in the Black-Scholes Model
What's the intuition behind the fact that the limit of $\mathcal{N}(d_2)$, i.e. the (risk-neutral) probability of exercise, in the Black-Scholes Model tends to $0$ when the volatility tends to ...
2
votes
3
answers
1k
views
Do basket options have a closed form valuation formula?
Suppose I'm simulating a European call option on a basket consisting of N stocks with slightly varying volatilities but all other parameters remain the same. From the perspective of an estimate, it ...
- 21
2
votes
1
answer
603
views
FX Euro-American Knockout Option Pricing
this is my first time asking questions here.
I want to look for some calculation method to price a very exotic option.
The FX Euro-American Knockout Option (EAKO) is an option that has an American ...
- 21
1
vote
1
answer
645
views
The greeks, vanillas and digitals
Question 1: I know website’s like: https://optioncreator.com/ display the pricing and payoff graphs of regular plain vanilla puts and calls. I would like to know if there is any website that displays ...
user59094
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 ...
- 585
34
votes
3
answers
8k
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 ...
- 605
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 ...
- 1,451
17
votes
5
answers
9k
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 ...
- 3,237
16
votes
4
answers
7k
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 ...
- 1,862
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.
...
- 1,886
11
votes
2
answers
6k
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 ...
- 5,749
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 ...
- 997
10
votes
3
answers
8k
views
How does an option's time value depend on moneyness?
How does an option's time value (also known as extrinsic or instrumental value) depend on how far it is in the money or out of the money? In other words, how does the time value change as the ...
- 585
9
votes
2
answers
1k
views
How to price an option allowing to change a call into a put?
A recruiter asked me this question:
Suppose you have the following contract:
a call option with maturity $T$ = 2 years
the possibility to change this call into a put at $t$ = 1 year
What is the ...
- 617
9
votes
1
answer
2k
views
Option pricing and mean reversion
In different books one can find a formula for option pricing when we assume that $\ln(S)$ follows a mean reversion process
$$ dS_t/S_t=\kappa(\theta-\ln(S_t))dt+\sigma dZ$$
If we calculate an ...
- 191
8
votes
2
answers
2k
views
Which process is the most commonly used for modeling stock prices?
I'm thinking of writing a master's thesis about pricing options using Levy processes, but I wonder if these processes are actually used for modeling stock prices or not (and which specifically)? And ...
- 433
8
votes
4
answers
10k
views
Basket option pricing: step by step tutorial for beginners
I would like to learn how to price options written on basket of several underlyings.
I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in ...
- 2,111