# 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 ...
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}{...
1 vote
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. (...
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 ...
124 views

### 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 ...
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 ... 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 ... 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), ...
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 ...
43 views

### 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
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 ...
105 views

### 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 ...
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 ...
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 ...
1 vote
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 ...
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 ...
235 views

### 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 ...
41 views

1 vote
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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 ...
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 ...
1 vote
164 views

### 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 ...
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 ...
1 vote
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
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) ...
118 views

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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
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 ...
1 vote
65 views

### 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 ...
54 views

### 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 ... 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 ...
141 views

### 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 ...
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)...
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 ...
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 ...