# Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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### Fitting parameters given an inverse function. (Orosi, 2015)

In trying to replicate Orosi's (2015) 5-parameter implied volatility model, but I can't wrap my head around the parameter fitting procedure Orosi proposes. My main goal is to calibrate the model to my ...
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4 votes
0 answers
195 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}{...
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1 vote
0 answers
91 views

### Price difference digital option : constant vol vs local vol

I got the following interview question: Consider a digital option, it will be priced by using two approaches: 1)constant volatility; 2)local volatility. At the strike, both volatilities are equal. (...
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2 votes
1 answer
70 views

### Do single name stock option volatility surfaces exhibit steeper volatility smiles after stock price crash episodes?

In index options, there was not much of a smile (on the put-side) until the 1987 market crash. I'm wondering if the same applies to single name stocks? That is, do price crashes in individual stocks ...
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5 votes
0 answers
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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 ...
• 13.9k
-1 votes
2 answers
187 views

### One touch UP no touch DOWN, One touch DOWN no touch UP [closed]

I was reading about exotic options and I came across something new. One touch down no touch up option and the other one I saw was One touch up no touch down option. I would like to understand how it ...
2 votes
1 answer
131 views

### Probability of touching short call strike and not touching touching short put strike of a short strangle?

I just came across a blog post. I believe the answer is a correct approximation: http://tastytradenetwork.squarespace.com/tt/blog/probability-of-touching-both-sides I modified the question in the post ...
2 votes
2 answers
157 views

### Gaussian copula calibration to option price

I have an "exotic" option that is a function of two interest rates (say 3m Libor at 1y maturity and 2y maturity). I assume both the rates follow sabr model (already calibrated to vanillas), ...
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2 votes
1 answer
89 views

### How to compute the Present Value of this path-dependent option?

I have an option whose payoff depends on its value at two times $T_1$ and $T_2$ as follows. $$V(t) = \mathbb{E}^{Q}[\mathbb{1}_{S(T_1)>B} (S(T_2)-K)^+)],$$ where the stock price follows the GBM ...
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0 votes
0 answers
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### Valuing a call option that is issued today, exercisable after 2 years from the issue date and expires 3 years after the issue date

if we assume: Current price: $0.25 Exercise price:$0.25 life: 3 years Risk free rate p.a: 0.2% volatility p.a: 85% The option cannot be exercised within the first 2 years, after 2 years, it is ...
1 vote
0 answers
70 views

### Option pricing under Vasicek, CIR, H-L and BDT model

I have implemented and calibrated recombining trees on Excel for the Vasicek, the Cox-Ingersoll-Ross, the Ho-Lee and the Black-Derman-Toy model. I now would like to price some options with these ...
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0 votes
0 answers
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### Discrete geometric asian option, analytic vs MC

I am attempting to price a discrete geometric Asian option using both the closed form formula (can be found in section 3.2.2 of 'Monte Carlo methods in Financial Engineering' by Glasserman) and an MC ...
0 votes
1 answer
77 views

### Floating lookback put, MC vs analytic

I am attempting to price a floating lookback put using the analytic formula. (eg. can be found in Shreve's vol II stochastic calculus section 7.4 or on Wikipedia) and wish to confirm the result by ...
3 votes
1 answer
241 views

### Bergomi Volatility Model

I was studying on the Bergomi volatility model(using forward variance represented as $\xi_{t}^{T}$).However I don't understand how the author passes from the sde to the first step by only integrating ...
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1 vote
0 answers
56 views

### HNGARCHFIT in R (No standard deviations or P values printed)

When I estimate an HN-GARCH model using the hngarchfit() from the fOptions package in R, only the coefficient estimates are printed. There are no standard deviations or P-values printed. Does anyone ...
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3 votes
2 answers
654 views

### How do you derive this Carr-Madan-like equation?

How do you derive equation (3) below? The equation is tagged as equation (11) in this paper: http://janroman.dhis.org/finance/IR/Heston%E2%80%93Hull%E2%80%93White%20Model%20Part%20I.pdf There are ...
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0 votes
1 answer
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### Correlation effect in Quanto options

My question will probably be stupid but here it is. I try to understand the effect of the correlation between exchange rate and underlying in a quanto option. And to have a non-precise understanding ...
0 votes
1 answer
41 views

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1 vote
1 answer
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### Replicating Portfolio / Complete Market / Attainable Claim

Attempt So Far: 1) First Part: I have shown that the market is arbitrage-free since the only possible portfolio for which $V_1^h\geq0 \$ given that $V_0^h=0 \$ is $h=(0,0,0)$ and this clearly ...
3 votes
2 answers
280 views

### EPE for interest rate swap

Hey how to calculate Expected positive exposure in the case of interest rate swap? Assume that I simulate $M$ interest rate paths for time grid $0=t_0\le t_1 \le ... \le t_N = T.$ What is the ...
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1 vote
0 answers
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### Index CDS Option (Spread Quoted) - Black's Formula

I have looked at the question and answers here and I have read Chapter 11 of Dominic O'Kane's book Modelling Single-name and Multi-name Credit Derivatives. The book is very clear and has some in-depth ...
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8 votes
1 answer
532 views

### Bermudan Swaptions - Payer vs. Receiver (LGM)

There is abundant literature discussing the pricing of Bermudan swaptions and the relevance of single-factor Markov-functional models (e.g. LGM) versus multi-factor market models (e.g. LMM). From a ...
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1 vote
1 answer
156 views

### Calibration of Heston model with stochastic short rate

I have following Heston model with stochastic short rate: \begin{eqnarray*}dS\left(t\right)&=&r\left(t\right)S\left(t\right)dt+\nu\left(t\right)S\left(t\right)dW^{S}\left(t\right)\\dr\left(t\...
1 vote
3 answers
187 views

### How to price a call option with long maturity (5 to 10 years)

I am trying to find the industry accepted method on how to price a long term American call option (maturities 5 to 10 years) on an underlying which is an accumulation fund (so no dividend payouts) ...
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2 votes
1 answer
118 views

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1 answer
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### Black Sholes Options Pricing Clarification Questions [closed]

I am interested in pricing American Call and Put Options using BSM and I am new to exploring options prcing. I have some questions here that would really remove the confusion I have on how to more ...
1 vote
0 answers
39 views

### Black 76 and Asian Style Options on Shaped Power Futures

I am attempting to price a monthly lookback option on the gen-weighted average price of power at a particular solar plant over a given month. If the option settles at hub H, am I right to shape the ...
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1 vote
0 answers
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### Any research paper further studying the conclusions given by Derman Regimes of Volatility

As we know Emanuel Derman mentioned 3 different market conditions where sticky delta, sticky strike, and sticky implied tree are relatively best suited. Are there any relevant research paper further ...
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0 votes
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### Volatility for options pricing: fixed window or match maturity?

When calculating the volatility or covariance matrix of stock returns for the purpose of pricing a vanilla option on an underlying, it is difficult to choose the window over which the volatility ...
6 votes
1 answer
173 views

### 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 ...
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### What is the relationship between Vanna and Gamma?

I'm trying to build a crude model for the effects of delta hedging on major indices like the S&P 500. My background is more in pure mathematics so a lot of this stuff is new to me. That said I ...
2 votes
0 answers
205 views

### Implementing a Variance Swap Hedging in R

I am trying to compute a hedge for a variance swap, in a simulation. Fo that I am using the following equation:\begin{align*} E^Q\bigg(\sum_{i=1}^n \bigg(\frac{S_{t_{i}}-S_{t_{i-1}}}{S_{t_{i-1}}}\bigg)...
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3 votes
1 answer
242 views

### What is the Radon-Nikodym derivative in the Heston model?

It is clear to me that $$\frac{dQ}{dP} = e^{-\lambda W_T-\frac{\lambda^2}{2}T}$$ is the Radon-Nikodym derivative that defines the change of measure in the framework described by Black and Sholes. But ...
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0 votes
0 answers
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### Is the market price of risk deterministic or stochastic in the Heston model?

I am recently digging into the Heston model and I have noticed that every author refers to the market price of risk simply as $\lambda$, or sometimes it is more clearly specified to be bi-dimensional ...
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