Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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145 views

Relationship between VIX and Vega

Assuming that all other factors (such as underlying price, strike price, etc.) remain unchanged, I want to see how a spike in VIX would affect the price of the average call option? Assume Vega is ...
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1answer
69 views

Autocallables under LSV

I’m looking at prices of Autocallables under Local vs. Local-Stochastic volatility. The stochastic part of my LSV model is driven by the Heston model. Increasing the volatility of variance parameter ...
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0answers
35 views

Question on model recalibration upon a spot shift scenario analysis

I am given a plot of the fair value of a complex derivative against a scenario spot shift for a range odd possible shifts (-40% to 40%). Let us say the pricing model is a local vol model. I am unable ...
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2answers
61 views

Delayed Settlement Option- how will values in Black Scholes change

If there is an option that expires a year from now, but is settled after 2 years, how would the Black Scholes formulation for such a situation look like? Will the risk free rate now be for 2 years or ...
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1answer
47 views

change in implied volatility with respect to change in spot

It's clear that IV increases as spot decreases, and vice-versa. In pricing an option, is there any model that is useful in estimating the change in IV with change in spot price? For example, if the ...
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0answers
32 views

Industry standards for vol control index options

Consider an index of the type: $I(t)/I(t-1) = 1+ a(t) (S(t)/S(t-1)-1)+(1-a(t))r(t-(t-1))$ It is arbitrarily initialized. $r$ is the risk free rate. a(t) is determined piecewise as: $a(t)=s_{target}/s_{...
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46 views

Monte Carlo Simulation of GBM Process has a Very High Variance - Explanation Needed as to why?

I use Geometric Brownian Motion (GMB) to simulate a share price from March 24, 2020 to March 24 as follow: \begin{equation} S_t=S_{t-1}exp((rf-0.6\sigma^2)*(2)+\sigma*sqrt(2)*\mathcal{N}(0,1)) \end{...
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0answers
120 views

Derivation of Bergomi model

In Stochastic Volatility Modeling, L. Bergomi introduces in Chapter 7 the pricing equation (7.4) : $$ \frac{dP}{dt}+(r-q)S\frac{dP}{dS}+\frac{\xi^t}{2}S^2\frac{d^2P}{dS^2}+\frac{1}{2}\int_t^Tdu\int_t^...
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108 views

Exotics - Combination of different payoffs using Black-Scholes

I'm currently struggling with the derivation of a formula to price the following exotic option with Black-Scholes. The option has the maximum payoff of $(S_T-z)$ and $(y - S_T)$, where $S_T$ is the ...
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48 views

Bergomi's model normalisation

On his book https://www.amazon.fr/dp/B019FNKQS8/ref=dp_kinw_strp_1 Bergomi derives a multifactor mean reversible volatility of the volatility such that : \begin{equation*} d \xi_{t}^{T}=\omega(\tau) \...
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1answer
142 views

Understanding Monte Carlo to solve option price with local volatility

I have read this question pricing using dupire local volatility model which seems to have an answer from here https://www.csie.ntu.edu.tw/~d00922011/python/cases/LocalVol/DUPIRE_FORMULA.PDF Both of ...
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1answer
159 views

Why does volatility increase the expense of delta-hedging?

Consider someone that writes a call, and wishes to delta-hedge against it to remain delta neutral. For this to be profitable, the price they sell this option for should be greater than or equal to the ...
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76 views

Black-Scholes option pricing [duplicate]

Consider Black-Scholes (B, S) market model. Let $r = 0$ (hence, $B_t ≡ 1$), $S_0 = 0 $. Stock price is described by $dS_t = σS_tdW_t$. Find the price of the option that pays $(S_T^3 - S_T^2 )_+ = max(...
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71 views

Why is the interest rate risk secondary for a vanilla equity option?

Consider the vanilla payout: $Max(S(T)-K,0)$ priced under the RN measure as: $E[e^{-rt}Max(S(T)-K,0)]$ which under no dividend/borrow assumption equals $E[e^{-rt}Max(S(0)e^{rt}X(T)-K,0)]$ for $X$ ...
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1answer
354 views

Fourier transform of a European put

In book The concepts and practice of mathematical finance, in the context of illustrating the stochastic volatility model, the Fourier transform $\hat{P}(\xi, V, T)$ of a European put $P(x, V, T)$ is ...
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1answer
86 views

SDE into ODE problem

Let S be the solution of the SDE: $dS_t = g(S_t)dt + \sqrt S_tdW_t, \; S_0 ∈ (1, 2)$, where $g(·)$ is a bounded function. Let $τ$ be the exit time $τ = min(t ≥ 0 : S_t ≥ 2 \; or \; S_t ≤ 1)$. Obtain ...
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1answer
65 views

Finding Option Probability Density Using Local Volatility from Dupire Model

This question is different than pricing using dupire local volatility model and Is Dupire's local volatility model path independent to recover historical option price? I also asked this on Math ...
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0answers
26 views

Generate a Fractional Gaussian Noise

I am trying to simulate a Fractional Gaussian Noise using Fast Fourrier algorithm.However,I couldn't even if I could retrieve my original covariance matrix such : $E\left[ X(t)X(s) \right] = \frac{1}{...
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1answer
89 views

Deriving the Heston-Hull-White PDE

I'm trying to derive the Heston-Hull-White PDE. The correct backwards PDE is equation (1.3) of this paper on page (2). I will begin deriving the forward PDE, but switching between the two is trivial. ...
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1answer
52 views

In what cases characteristic function of (log-)price process is known?

Hey I know that we can use characteristic function of log-price process to price different options. But when we know the characteristic function? I know that we can take Levy processes and constant ...
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1answer
549 views

How to simulate Levy processes

Hey how to simulate Levy processes? I have no problem with Wiener process and compound Poisson process, I also know how to simulate Variance Gamma process but I have no idea how to simulate for ...
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0answers
56 views

Calendar arbitrage with dividends

In this question, it is shown: i) the definition of calendar arbitrage for Call options; ii) the financial/mathematical rationale. Nevertheless, in that question, one assumes that there are no ...
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0answers
36 views

how can properties of transition matrix be applied in the transcation cost of option

I am currently reading the PP BOYLE's article ' Option Replication in Discrete Time with Transaction Costs' written in 1992. Here is one place i couldn't figure out: Where does that $\widehat{p}$ ...
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1answer
70 views

FX Asian Option Moment-matching in Harmonic case

I need to price a "foreign-paying" fixed-strike Asian (i.e., average) option. Thus, the payoff is: $$\left(\frac{A_T - K}{A_T}\right)^{+} = \left(1 - \frac{K}{A_T}\right)^{+} = K \left(\frac{...
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1answer
60 views

Why does bull call spread shows higher payoff than bull put spread?

I am trying to compare bull call spread and bull put spread for equity index option. For the options where the put call parity holds, I am getting a different payoff for bull call spread and bull put ...
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3answers
265 views

How to derive a pricing PDE for an asset that follows a mean-reverting process?

I want to derive a Black-Scholes type partial differential equation to price options on an asset that follows a mean-reverting process (Schwartz model). My attempt follows the methodology of deriving ...
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1answer
136 views

Barriers on structured notes

I asked a question here: Structuring and Customization Thanks to all the contributors. However, I now have a follow-up question. I would like to buy barrier options and I was informed from that post ...
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2answers
251 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? ...
1
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1answer
49 views

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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0answers
106 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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66 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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1answer
62 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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90 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 ...
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2answers
107 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
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1answer
92 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
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2answers
133 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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45 views

How to match simulated local vol european prices with closed formula

Say an implied volatility is given by $\sigma_{imp}(T, log(F_T/K))$ and we note the Dupire local volatilty $\sigma_{loc}(T, log(F_T/K))$ with $F_t$ the forward rate and $K$ the strike. The price of a ...
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1answer
83 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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34 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 ...
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0answers
41 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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0answers
26 views

No standard deviations using the hngarchFit function in R [duplicate]

I am trying to estimate a HN-GARCH model in R. However, when using the hngarchFit() function in R, no standard deviations for the coefficients are printed. I have looked at the function behind the ...
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0answers
60 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 ...
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1answer
69 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
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1answer
163 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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0answers
42 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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2answers
414 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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1answer
80 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 ...
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1answer
26 views

Valuing Conditional “All Or Nothing” Multi Asset Options

I would like some insight as to how to value modified rainbow options on multiple assets: For example: A multi asset option, Call GOOG with $S_t$ \$1600 that you may exercise if and only if you also ...
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1answer
145 views

Why does the price of an option increase with increasing Rho?

I was wondering why the price of an option increases with Rho (price change for a derivative relative to a change in the risk-free rate of interest). I found this explanation on a website: "Each ...
2
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1answer
64 views

European call option lower bound derivation by Black-Scholes formula [closed]

Derive the lower bound of european call options: $$C(S, t)\geq[S-e^{-r(T-t)}K]^+$$ I know how to derive it using put-call parity, but is there any way to derive from Black-Scholes formula?

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