# Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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### 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 ...
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 ...
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 ...
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 ...
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 ...
32 views

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_{... 0answers 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{... 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^... 0answers 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 ... 0answers 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) \... 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 ... 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 ... 0answers 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(... 0answers 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 ... 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 ... 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 ... 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 ... 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}{... 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. ... 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 ... 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 ... 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 ... 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} ... 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{... 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 ... 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 ... 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 ... 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? ... 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 ... 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}{... 0answers 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. (... 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 ... 0answers 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 ... 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 ... 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 ... 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), ... 0answers 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 ... 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 ... 0answers 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: $0.25 life: 3 years Risk free rate p.a: 0.2% volatility p.a: 85% The option cannot be exercised within the first 2 years, after 2 years, it is ... 0answers 41 views ### Option pricing under Vasicek, CIR, H-L and BDT model I have implemented and calibrated recombining trees on Excel for the Vasicek, the Cox-Ingersoll-Ross, the Ho-Lee and the Black-Derman-Toy model. I now would like to price some options with these ... 0answers 26 views ### No standard deviations using the hngarchFit function in R [duplicate] I am trying to estimate a HN-GARCH model in R. However, when using the hngarchFit() function in R, no standard deviations for the coefficients are printed. I have looked at the function behind the ... 0answers 60 views ### Discrete geometric asian option, analytic vs MC I am attempting to price a discrete geometric Asian option using both the closed form formula (can be found in section 3.2.2 of 'Monte Carlo methods in Financial Engineering' by Glasserman) and an MC ... 1answer 69 views ### Floating lookback put, MC vs analytic I am attempting to price a floating lookback put using the analytic formula. (eg. can be found in Shreve's vol II stochastic calculus section 7.4 or on Wikipedia) and wish to confirm the result by ... 1answer 163 views ### Bergomi Volatility Model I was studying on the Bergomi volatility model(using forward variance represented as$\xi_{t}^{T}$).However I don't understand how the author passes from the sde to the first step by only integrating ... 0answers 42 views ### HNGARCHFIT in R (No standard deviations or P values printed) When I estimate an HN-GARCH model using the hngarchfit() from the fOptions package in R, only the coefficient estimates are printed. There are no standard deviations or P-values printed. Does anyone ... 2answers 414 views ### How do you derive this Carr-Madan-like equation? How do you derive equation (3) below? The equation is tagged as equation (11) in this paper: http://janroman.dhis.org/finance/IR/Heston%E2%80%93Hull%E2%80%93White%20Model%20Part%20I.pdf There are ... 1answer 80 views ### Correlation effect in Quanto options My question will probably be stupid but here it is. I try to understand the effect of the correlation between exchange rate and underlying in a quanto option. And to have a non-precise understanding ... 1answer 26 views ### Valuing Conditional “All Or Nothing” Multi Asset Options I would like some insight as to how to value modified rainbow options on multiple assets: For example: A multi asset option, Call GOOG with$S_t$\$1600 that you may exercise if and only if you also ...
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?