Questions tagged [option-pricing]
Questions about models for the valuation of option contracts.
1,777
questions
0
votes
0
answers
18
views
Binomial Option Pricing [duplicate]
We are currently working on the "standard" binomial option pricing. If the market agrees that a specific stock will raise by, let's say, 90% next period. At first glance, this seems to have ...
- 1
1
vote
1
answer
64
views
When does a closed form analytic solution exist/not exist for the value of an option given by the BS eqn?
I am new to the quantitative finance side of things( came from mathematical physics). I'm currently investigating numerical techniques for solving BS, which made realise when are numerical techniques ...
- 11
3
votes
0
answers
122
views
Continuation value in Longstaff-Schwartz: Why the expected value?
In the paper by Longstaff and Schwartz on American option pricing, the continuation value at time $t_k$ is given by:
\begin{align}
F(\omega;t_k) = \mathbb{E}_Q\Big[\sum_{j=k+1}^Kexp\Big(-\int_{t_k}^{...
- 571
1
vote
0
answers
41
views
STOXX50 and VSTOXX joint calibration
I am currently researching the joint calibration problem of SPX and VIX. The idea is that: VIX options are derivatives on the VIX, which itself is derived from SPX options and should thus be able to ...
0
votes
1
answer
96
views
What is the risk neutral expectiation of an option price given a move in spot?
Lets say we have a volatility surface for the SPX at time t with spot S. We consequently know the price of some call option at maturity T with strike K. What is the risk neutral expectation of the ...
- 190
2
votes
0
answers
97
views
Problem matching prices of Black-Scholes vs. GARCH(1,1) in Duan (1995)
In the paper of Duan (1995) the author compare European call option prices using Black-Scholes model vs. GARCH(1,1)-M model (GARCH-in-mean). To be brief, the author fits the following GARCH(1,1)-M ...
13
votes
4
answers
399
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 ...
- 370
1
vote
1
answer
137
views
GARCH process simulation in R
I'm trying to learn how to simulate the GARCH(1,1) for option pricing using Monte Carlo. I need to learn how to code the equations for the stock log returns and the variance process. I'm trying to ...
0
votes
2
answers
151
views
Best tool to find an optimal option? [closed]
I like to sell uncovered put options, using my valuation of the company as the strike price. I'm looking for a tool that takes stock identifier and strike price as input and outputs the optimal ...
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
2
votes
1
answer
160
views
Pricing Quantos with Local-Stochastic Volatility model
I would like to price equity quanto options with the Heston Local-Stochastic Volatility model (LSV) but I am having hard time understanding how to apply quanto adjustment in such complex setup.
When ...
- 21
2
votes
0
answers
100
views
Exact delta-hedging for endogenous payoffs
I would like to derive the exact delta-hedging strategy in the Black-Scholes market to replicate the following non-standard endogenous payoff. The particularity is that the payoff does not only depend ...
- 267
0
votes
0
answers
71
views
Theta Greek Max Curvature [duplicate]
how to solve it for max Theta Curvature?
i'm looking for the pure math glyph formula..
it may be related to actually
3rd deriva & curvature function..
- 1
2
votes
1
answer
398
views
Gamma for a basket option in Python - Finite Differences vs. AAD Autograd library using Heaviside Approximation
I have been trying to use the Heaviside Approximation for a simple basket option so that I can solve for Gammas with AAD (Adjoint Automatic Differentiation). This routine smooths the payoff function ...
- 139
0
votes
2
answers
259
views
What is the Fair Strike in a Var/Vol Swap and how does it relate to its price? [closed]
I am a student trying to price volatility and variance swaps.
People who price those two products usually try to get the "fair strike", and don't seem to care about the price.
However, I ...
- 1
0
votes
1
answer
80
views
Solve for spot price given delta [closed]
I can use Black Scholes or Bjerksund Stensland to solve for delta given spot price, strike, expiration, vol, interest rate, etc. But is there a direct solution to solve for spot price given delta, ...
- 103
0
votes
0
answers
30
views
Binomial model returning linear IV smile when estimating for IV
So I've been attempting to align the Binomial model with the American put option price so that I can calculate accurate Greeks taking into account the optimal exercise boundary of these options. The ...
- 1
0
votes
0
answers
49
views
Monte Carlo Derivative Pricing
In order to try and price some derivatives with payoff $H(S_T).$
I am going to calibrate a few models (BS, Heston and CEV) to some real world data. Then I will calculate option prices as follows:
...
- 101
2
votes
1
answer
259
views
Question on Merton's self financing derivation
I'm reading Merton's Optimum Consumption and Portfolio Rules in a Continuous-time Model, and don't understand the step where he goes from discrete to continuous time. Specifically, my confusion is ...
- 165
2
votes
2
answers
320
views
Intuition behind calendar spread max loss
With a calendar spread (buying back, selling front), max loss is defined as some variant of "maximum potential loss is the cost of opening the trade (Premium Paid − Premium Received = Total Debit)...
3
votes
2
answers
1k
views
Theta changes over time
Theta is the change of an options value with respect to time. But theta itself changes over time. Today's option theta is not the same as tomorrow's option theta. What is the greek name for this value?...
0
votes
0
answers
77
views
How to improve fit in American options vol surface?
I am trying to model the volatility surface of index etfs (spy, iwm and qqq). I am using the CRR model with discrete dividends and the spot model. I find that for some cases there is a noticeable ...
- 190
1
vote
0
answers
104
views
Why fitting $\mathbb{Q}$ vs $\mathbb{P}$ measure Heston model if both fit to market
If both models fit their closed form formulas to market prices, why should I prefer a more complex model? ($\mathbb{Q}$ version has one extra parameter $\lambda$)
Do valuation with dynamics work ...
2
votes
1
answer
196
views
Questions about the replicating portfolio in the binomial model
I'm starting to teach myself quantitative finance and I've got several questions (marked in bold) regarding the replicating portfolio of a security in the binomial model. I'm following, among others, ...
- 131
1
vote
1
answer
394
views
Basket option value calculation
I am reading the article, where different approximations for the pricing of basket options are presented. I have tried to reproduce the result obtained by the Gentle's method in Python.
We define the ...
- 239
0
votes
2
answers
332
views
Risk free rate for currency option
I’m trying to price a call option on EUR/GBP exchange rate and it expires in 1 year. Should I use GBP Libor as foreign risk free rate in order to apply BS formula? The pricing date is 02/21/2023 but ...
0
votes
0
answers
31
views
How to price an american put option on a dividend-paying stock? [duplicate]
There is no Black Scholes formula for the value of an American put option on dividend paying stock eithe has been produced ? Should I use the binomial model ?
- 31
1
vote
0
answers
42
views
Implying a probability distribution from option prices [duplicate]
I was reading this article, when I came across this text:
Without using a complex options pricing model, one can use intuition
to translate option prices into implied probabilities. For instance,
the ...
- 1,398
3
votes
0
answers
79
views
For derivatives pricing, does FEM actually ever outperform FDM?
Simple question that I was wondering about over during the weekend.
I have done a little FEM during the last years and my university time and did not spend a lot of time with FDM. For a new job I have ...
- 113
1
vote
2
answers
604
views
Butterfly price bound independent on underlying distribution
Assuming no fees and interest rate $r=0$%, what is the most you would be willing to pay for a \$103/\$106/\$108 European call fly, regardless of the underlying distribution? Buying the fly in this ...
- 155
0
votes
1
answer
137
views
Does Black-Scholes imply that the expected return for an asset is fixed as the volatility increases? [closed]
I'm new to this, and just trying to understand what options prices imply about asset growth. I'm looking at the following expression for the underlying asset price in the Black-Scholes model, in ...
- 111
1
vote
1
answer
353
views
Gamma and Theta of a swaption
For a swaption, I had 2 questions:
how would I guage the PnL based on RV vs IV on a swaption?
I'm guessing its 0.5 x gamma x (RV^2-IV^2)(or realized variance - implied variance)
Not 100% sure on ...
- 11
2
votes
1
answer
217
views
QuantLib including holiday in option price
I am trying to add a holiday to my calendar in QuantLib such that my option pricing model considers this in pricing where I would expect that the time to expiry should decrease with the inclusion of a ...
- 23
0
votes
0
answers
61
views
Time steps in CRR Binomial Option Pricing for American Options
how do you determine the time steps required as inputs to the Cox Rubinstein Binomial Option Pricing model when trying to determine the fair price of an American option? Most textbooks and literature ...
- 101
5
votes
2
answers
668
views
Pricing and hedging caps and floors on illiquid emerging markets
I'm tasked with the problem of setting up a cap/floor trading on an emerging market which doesn't have any interest rate derivatives traded yet besides plain vanilla interest rate swaps. We intend to ...
- 764
0
votes
0
answers
50
views
What is the meaning of Domestic Exchange Rate here?
So I have the following formula for the Pricing of a Quanto Option (see image below).
While I understand this formula pretty well, I am not sure what is referred to as "domestic exchange rate&...
- 1
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.
$$\ln(\textrm{atm vol}) = \...
- 31
0
votes
0
answers
64
views
Sticky Strike vs Sticky Delta - revisited [duplicate]
Given a time series of implied volatility smiles over the last 100 days for a given option (e.g. 1y S&P call, or 1y x 10y swaption), and the corresponding forward rates, what test should be ...
- 31
1
vote
0
answers
78
views
How can I derive the price of american options given the european options prices? [closed]
I have the european volatility surface of a given asset. What is the correct procedure to compute the price of the options with american exercise type?
- 190
3
votes
1
answer
157
views
Volatility model for pricing of Down-In Put options
What is the best volatility model to price Down-In Puts (DIP) under several stress scenarios (e.g downward movement of underlying price by -5%, -10%, -15%)?
Please note that I got the market prices ...
- 33
3
votes
1
answer
294
views
Right risk free rate to price an Option using BS formula
I understand this is very basic question but I still scramble to determine what would be right risk free rate to price a simple European call option using Black-scholes formula, with maturity is 5 ...
- 373
1
vote
0
answers
363
views
Implied volatility to local volatility via Dupire
I am doing some self study on stochastic local volatility modelling and am having a hard time replicating some results from the paper "FX Option Pricing with Stochastic-Local Volatility Model&...
- 11
0
votes
0
answers
70
views
Characteristic Function Kou (2002) Model
I'm looking for the correct characteristic function for the Kou (2002) jump diffusion model.
Can someone help me? Because if I try to look at it online everyone forgot $r$ and $S_0$.
This is what I ...
- 1
0
votes
0
answers
84
views
Price of financial assets at $t=0$ in Black-Scholes framework
Given the share price equation
$$
dS_t=rS_tdt+\sigma S_tdW_t
$$
working in the framework of Black-Scholes model, find the price at $t=0$ of the following two financial assets:
(a) The asset pays at $t=...
- 101
1
vote
0
answers
79
views
Calibration period
I want to calibrate some model to market data. This could fx be Bates, Kou, Black-Scholes, etc. So, for each model we have a set of parameters which need to be estimated through calibration. Now, my ...
- 59
0
votes
1
answer
195
views
Delta of a forward ATM option
Reading:
What are some useful approximations to the Black-Scholes formula?
I understand that a ATM Call option can be approximated to $$ C(S,t)≈0.4Se^{−r(T−t)}σ \sqrt{T−t}$$
Also, I often hear that an ...
- 365
2
votes
2
answers
949
views
How to understand wedge?
It is heard that trading wedges (cap/floor straddle - swaption) is actually trading the correlation btw forward rates. How to understand this? Either swaption or cap/floor seem to be insensitive to ...
- 51
2
votes
1
answer
299
views
How to find IV from market prices accodring to Bergomi
I was conviced to read Bergomis book on stochasic volatility to learn how options are traded in practice. He basically writes that the probabilisitc side is rather useless and that one only uses the ...
- 25
2
votes
1
answer
456
views
How is an exchange rate process a martingale under any measure?
Suppose a process for a stock price of a US-based company traded in the USA is, under the USD money-market numeraire:
$$dS_t=S_tr_{USD}dt+S_t\sigma_SdW_1(t)$$
Using fundamental theorem of asset ...
- 55
0
votes
0
answers
182
views
Can the break-even of a straddle be lower than the implied move?
Let us consider a two day option:
1 day having a baseline vol of 16%
1 day having an event for which we want to find the implied move, higher than 16%
Is it possible that the price of the straddle ...
- 53