Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
478
questions with no upvoted or accepted answers
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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 ...
- 4,553
28
votes
0
answers
630
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 $Q-$ ...
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12
votes
0
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474
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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 ...
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9
votes
0
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246
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Basket option density in BS model
Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
- 326
7
votes
2
answers
275
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Likelihood ratio and pathwise sensitivity method for coupled SDEs
I have two coupled SDEs
\begin{align*}
dS_t=rS_tdt+V_tdW_t^{(1)},\\
dV_t=aV_tdt+b(V_t)dW_t^{(2)},\\
\end{align*}
where $W_t^{(1)}$ and $W_t^{(2)}$ are independent Brownian motions, initial input data ...
- 609
7
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0
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204
views
Has a closed-form formula for the collateral choice option been found?
The collateral choice option problem has been formulated in e.g. Fujii and Takahashi (2011), Piterbarg (2012) or Antonov and Piterbarg (2013), as the computation of an expectation of the following ...
- 7,959
7
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0
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2k
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Arbitrage free smoothing of volatility smile - cubic spline - implementation procedure
I am studying the paper Arbitrage-Free Smoothing of the Implied Volatility Surface, from Matthias R. Fengler (https://core.ac.uk/download/pdf/6978470.pdf).
The problem I want to solve is much simpler ...
- 81
7
votes
0
answers
152
views
recent developments in American options?
I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem.
Is there any development in pricing American options during 2005-2016? (based ...
- 247
6
votes
1
answer
374
views
Importance sampling for Monte Carlo with local volatility in practice
I am given a diffusion with a local volatility to price barrier options:
$$dX(t)=X(t)\mu dt+X(t)\sigma(t,X)dW_t$$
I want to use Importance Sampling to price barrier options "far" out of the ...
- 125
6
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0
answers
549
views
Libor Market Model with SABR Calibration
What is the industry practice in calibrating SABR Libor Market Model? Do you first calibrate the SABR model using market data and then implement the libor market model with the calibrated parameters?
...
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6
votes
0
answers
193
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Intuition behind the Carr and Wu (2014) static hedging for ordinary options
Let $(S_t)_{t \geq 0}$ be the price of an underlying asset, $r$ be the risk-free rate of return, $q$ the dividend yield, $C_t(K,T)$ is the price of a call option written on $S_t$ at time $t$ with ...
- 2,436
6
votes
0
answers
228
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Pricing interest rate options in emerging markets
I've been thinking how to price the early payment of mortgages in banks from emerging markets, where swaptions/caps/floors aren't available, and how to hedge this kind of options. At first I thought ...
- 185
6
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0
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405
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How are quants able to verify whether their calculated prices are any good
This question is related to the discussion on Model Validation Criteria
However it appeard to be very high level to me and I would like to go more into detail.
Not working at a pricing desk the ...
- 3,377
6
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0
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254
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Use of Local Times in Option Pricing
I know two applications of local time in option pricing theory.
First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
- 4,553
5
votes
0
answers
207
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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 ...
- 51
5
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0
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225
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Probability density from COS method too sensitive to truncation range
I have a long-standing confusion around the truncation range of the COS method proposed by Fang and Oosterlee because I find that the results are highly volatile given the different truncation ranges.
...
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5
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220
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Very close local volatility and implied volatility using Dupire's equation
I used Dupire's equation to calculate the local volatility as in https://www.frouah.com/finance%20notes/Dupire%20Local%20Volatility.pdf and Numerical example of how to calculate local vol surface from ...
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5
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183
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Why Vasicek model on a tree is a bad choice for pricing American option on credit prepayment?
I have an American option on a credit prepayment, i.e. the holder of the option can prepay the remaining credit if the interest rate falls below the initial strike. The pricing of this option was done ...
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5
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0
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144
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Integrated Delta does not seem to be smooth (ATM, Heston)
I am interested in an integrated call option that removes the dependence on time, $$I(S)=\int_0^\infty C(S,t)\text{d}t.$$ Because the value of a call option is a smooth function, I expect this ...
- 15.2k
5
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0
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583
views
Implied Funding/Borrow Costs in Short-Dated ETF Option Prices
I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
- 344
5
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0
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235
views
Pricing and hedging of vanilla options based on non-tradable underlying
Consider a non-tradable stock index $S$ which satisfies:
$dS_t=\mu S_tdt+\sigma S_tdW_t$
and a risk-free asset $B$.
I want to price an European Call option with the payoff $C_T=max(S_T-K,0)$. The ...
- 61
5
votes
0
answers
147
views
Complete Financial Market: Integrability condition for Contingent Claims
Consider an arbitrage-free and complete financial market with underlying filtered probability space $(\Omega,\mathcal{F},\{\mathcal{F}_{t}\}_{t\,\in\,[0,T]},\mathbb{Q})$, where $T\in(0,\infty)$ is ...
- 51
5
votes
0
answers
322
views
pricing option with two stocks
Let $\left(S_t^{(1)}\right)_{t\ge0}$ and
$\left(S_t^{(2)}\right)_{t\ge0}$ be the price processes of two stocks
with dynamics
$$ \begin{align}
& dS_t^{(1)}=\sigma_{11}S_t^{(1)}dW_t^{(1)}
\...
- 245
5
votes
0
answers
304
views
Quantitative approaches to measuring the effectiveness of a Stock Option Pricing Model?
My question contains many parts, but I will try to keep it somewhat focused. I am primarily looking for a framework to evaluate the accuracy of a stock-focused Options Pricing Model. One of the ...
- 1,872
5
votes
0
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354
views
Algorithmic Trading Model Calculation and Stale Data
I'd like ask everyone a more concurrency programming but definitely quant-finance related question. How do you deal with staleness of data in market hours as quote ticks are streaming and your model ...
- 131
5
votes
0
answers
701
views
Pricing with collateral
I have been confused about many things concerning the princing of securities with collateral.
We can prove that today's price of a security( fully collateralized and within the same currency) is the ...
- 51
4
votes
0
answers
70
views
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 ...
- 823
4
votes
0
answers
113
views
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 ...
4
votes
0
answers
335
views
Why calibrate volatility Models to volatility surfaces rather than underlying's historical price data?
I'm trying to grasp the rationale for calibrating stochastic volatility models (i.e. Heston model) to empirical IV data from market prices. Doesn't this assume that the options are fairly priced and ...
- 41
4
votes
0
answers
313
views
Characteristic function of the Bates model
I have a misunderstanding concerning the derivation of the SVJ model :
Firsty,I understand how to reach the final differential equation from :
\begin{gather}
dS_t = (r - q - \lambda t (e^{m-\frac{\nu}{...
- 446
4
votes
0
answers
322
views
Bates Model on Quantlib
I am actively trying to price an option using bates model on Quantlib.However,when I input my volatility I find the same Black Prices with the basic Heston Model.I wanted to know if my code was right.
...
- 446
4
votes
0
answers
123
views
Pricing of strange Asian lookback option with European-style payoff $\max\{ \max_{u\in[0,T]}S_u-\frac1T\sqrt{\int_0^TS_t^2\mathrm{d}t},0\}$
I am trying to price the Asian lookback option at time $t$ with time-$T$ (European) payoff $\max\{M_T-A_T,0\}$, where $$M_t=\max_{u\in[0,t]}S_u,\quad A_t=\frac1t\sqrt{\int_0^tS_u^2\mathrm{d}u},$$
and $...
- 609
4
votes
0
answers
120
views
Continuous option pricing: Brownian Bridge
I have a question on the proof of the formula of Sup(S) between 2 simulation points.
Do you know how the prove the following formula? Thanks
- 41
4
votes
0
answers
265
views
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-...
- 51
4
votes
0
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122
views
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}^{...
- 98
4
votes
2
answers
543
views
Simulation scheme for SABR beside the standard Euler discretization
QUESTION:
Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics?
Simulation that will withstand even for high volatilities....
- 1,627
4
votes
0
answers
737
views
How to price the american options using local volatility
I have given with a surface of american option prices $C_{am}(T, K)$. From these american option prices the implied volatility surface is deduced.
Now I want to find the local volatility $\sigma(s,t)$...
- 532
4
votes
0
answers
187
views
Is there an arbitrage free option model that treats volatility as a deterministic function of strike?
I am trying to get a good understanding of the different models out there, and thus be able to study hedging errors, and strengths and weaknesses. My understanding of the Local Volatility model in ...
- 707
4
votes
0
answers
124
views
Two barrier options puzzle
I come across an interesting question about barrier option as shown below.
Two barrier options are given with the same parameters including the barrier level. The first one is knocked out when it ...
- 55
4
votes
0
answers
225
views
Stochastic Long-Run Mean Instantaneous Variance in Heston Model (and extensions)?
I'm working on my dissertation in Financial Economics, focusing on the topic of Stochastic Volatility Jump Diffusion models; and I'm playing around with some ideas for model extensions. In particular, ...
- 41
4
votes
0
answers
149
views
Why does risk-neutral price processes do not, in general, compose all arbitrage-free price processes?
I was reading reviewing my mathematical finance notes and I came across a remark I cant understand fully
Remark :Contrary to discrete time models, the risk-neutral price processes do not, in general, ...
- 141
4
votes
0
answers
159
views
Pricing a Double Knock In Option
I have been looking at pricing a barrier option that has payoff of your usual European Call option, $\max(S_T - K, 0)$ if the stock price exceeds a horizon $A$ and then afterwards drop under some ...
- 151
4
votes
0
answers
114
views
Structured Energy Option Pricing
Let's say I have an option with the following terms. This is for an energy product (ie natural gas)
The contract will last for 6 months
The payoff is the difference between the first of month index ...
- 83
4
votes
0
answers
113
views
Spread in Option Quotes
Let's take a look at market-maker's option quote in vol terms: 8.5 / 9.5. In that example bid-ask spread equals 1.0 point of vol.
Can anybody clarifying how market-maker choose amount of spread in ...
- 41
4
votes
0
answers
118
views
ODE Solution in Carr's Randomized American Put
In Carr's 1998 paper Randomization and the American Put, he sets up the following ODE for the value of an American put with expiration given by the first jump time of a Poisson process with rate $\...
- 2,778
4
votes
0
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155
views
How can a beginner trader make use of 'volatility of volatility'
For a beginner option trader in equity options, how can he use this metric that is provided by his broker/data vendor?
How can he use this metric to gain an added understanding of the option pricing/...
- 1,394
4
votes
0
answers
284
views
negative transition probabilities in the heston model
I've been trying to implement a bivariate tree for pricing american options with the heston model in R using the paper of Beliaeva and Nawalkha (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
- 41
4
votes
0
answers
663
views
ATM volatility versus OTM volatility and directional standard deviation
The forward instrument vol curve is skewed to the downside (50 delta risk reversal, 25 put, 25 call) were trading several ticks to the put).
Is there a smaller standard deviation (in price terms) to ...
3
votes
0
answers
136
views
Models for tick-by-tick / high-frequency data
I've spoken to one or two persons at some market making shops, and I'm under the impression that for modelling tick data, aside from the rise of ML, a pure jump process such as the variance gamma ...
- 1,739
3
votes
0
answers
65
views
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 ...
- 31