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Questions about models for the valuation of option contracts.

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32 views

About Fourier-Based Option Pricing

I'm reading the book "Derivatives Analytic with Python" by Dr. Yves Hilpisch, chapter 6 Fourier-Based Option Pricing. From page 98 to page 101, the Lewis(2011) Approach was presented. I could follow ...
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23 views

Probability of touch (option) for security

I read through a few related threads on quant stackExchange. Similarly, I am looking for the probability of a security touching $X$ (strike points away) before an expiry time, $T$. From thread here: ...
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23 views

AFV Model Implementation for Convertible Bonds

I am reading the original AFV model paper for pricing convertible bonds. https://cs.uwaterloo.ca/~paforsyt/convert.pdf The paper is very technical and I am having trouble finding the actual PDE's to ...
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42 views
+50

Compo Feature in Asian Option on Futures

I'm pricing an Asian option on futures using Turnbull–Wakeman (other suggestions welcome) where the average is defined as $A _ { t _ { 1 } , t _ { n } } ^ { A , f } = \frac { 1 } { n } \sum _ { i = 1 }...
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0answers
32 views

Does it make sense to calculate an option price in future (at t+1)?

Often I ask myself whether it makes sense to calculate the price of a Call at t+1 supposing for example that underlying asset does no move i.e. $S_{t+1} = S_{t}$ ...
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13 views

Pricing options with 0 or negative underlying values

I am trying to calculate the value of an option whose underlying is the calendar spread between two months for a commodity (front month Brent vs 2nd month), usually known as a calendar spread option. ...
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1answer
70 views

Option greeks as dollar P&L

If I write the value of an option as O(S, K, T, V), where S is the underlying price, K is the strike, T is the time to expiry and V the implied volatility, how can I compute the dollar amount that I ...
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18 views

Black 76, finding current forward price and interest rate for a commodity option

Lets say the commodity in question is gas, flowing everyday for a period of time, and my curve data format is "DataEntryDate, FlowingFrom, FlowingTo". To get the forward price should I find the most ...
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81 views

Measure theory in quantitative finance

When I read up on stochastic modeling, the use of "measure" comes up a lot. So far I just read the word "measure" as "probabilities" or "distribution" and was able to get away with it when trying to ...
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28 views

how to derive vol curve for cross rate

For example I can get vol curves for two assets, say XAU/USD and XAG/USD for time T, I can calculate their asset correlation, obtain probability dension functions. Is there a proper way to synthesize ...
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0answers
21 views

How does REG-T apply to non-standard option strategies

I'm trying to estimate the margin impacts from non-standard (e.g. not in the CBOE manual) option strategies. How do the rules apply to things like this: (All European) ...
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103 views

Is there a relationship between Risk Neutral Pricing framework and Nash Equilibria?

Based on the Fundamental Theorem of Asset Pricing, the risk neutral price of a contingent claim on an asset in a liquid, arbitrage free market can be determined by switching to an equivalent $Q-$ ...
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0answers
26 views

Relation between one touch and binary option

Is there a relation between the price of a one touch option and the price of a binary option? By one touch option, I mean an option that pays off a fixed amount if the price of the underlying is ...
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1answer
75 views

Estimating at-the-money volatility where at-the-money option is absent from the market

I am trying to estimate the intraday ATM volatility in a market where the the strike prices are relatively sparse thus the ATM option may not exist (let's say the closest strike is about 2% away from ...
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0answers
34 views

Question about derivation of SABR volatility formula in original paper 'Managing Smile Risk' by Hagan et al

I have a question regarding the starting point of the derivation of SABR volatilities formulas in the appendix of the famous paper 'Managing Smile Risk' by Hagan et al. To derive SABR volatility ...
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0answers
53 views

Best Way of Interpreting Black-Scholes Formula [duplicate]

I'm curious to know the best interpretation of the Black-Scholes formula for a European equity call option: $$C(S,t)=S_tN(d_1)-Ke^{-r(T-t)}N(d_2),$$ where $d_1=\frac{1}{\sigma\sqrt{T-t}}\big[\ln(\...
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2answers
38 views

Modeling exercise notice time using lattices?

I am interested in modeling callable (say European) bonds which have a time gap between when the future call exercise is decided and when the call actually occurs (payoff) - say 7 business days. I am ...
2
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1answer
132 views

Quanto pricing explanation

I have paths generated from Heston, correlation Eq/FX, FX ATM vol but then I'm struggling to find the correct methodology. I tried to adjust the dividend in asset paths from my Heston Monte Carlo by ...
3
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1answer
140 views

Pricing and hedging fund-linked derivatives

I am looking for info regarding pricing, and hedging (notably vega and delta) of derivatives on funds. Could you please confirm/complete the below information I believe I've understood so far, or ...
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1answer
38 views

Develop a pricing formula for an American digital put option

This problem comes from concepts and practice of mathematical finance by Joshi Chapter 8 problem 9. Develop a pricing formula for an American digital put option Joshi's solution - He states that ...
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75 views

Beginner question on Black Scholes

Would you please confirm whether my understanding is correct please? (Sorry a lot of questions...) 1) BS is derived based on the assumption that during an infinitesimal time, we can replicate the ...
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1answer
71 views

Upper bound option price in volatility dimension

All, I have a theoretical question about the value of an option when spot price goes to infinity as a function of volatility going to infinity. I know that for a call option: The option value ...
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0answers
42 views

Difference end-of-day price and closing price of option

Is there a difference between end-of-day prices of an option (e.g. Barclays VXX) and the closing price of that option? If so, what is the difference. I cannot find anything clear about this anywhere, ...
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1answer
65 views

Using option pricing methods to model real asset liquidity

Liquidity risk (in the sense of asset exit risk) is warranted on investments that may not be easily divested at the going market or fair-value price. I am looking at a portfolio of private assets ...
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1answer
87 views

Software library: Pricing financial instruments, such as FX Forwards

I am currently reading material on how to price financial instruments such as FX Forward deals. One way of doing this seems to be by calculating its Fair Value³. This value can be split into two ...
2
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1answer
135 views

SABR PDE spot/forward upper boundary condition implementation

When running my Finite Difference code, I observe something odd. Although implementing a classical (non-reverting) SABR model, I initialized the variables such that it should be equal to Black-...
2
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0answers
22 views

z-score of an active return with a no-volatility benchmark

I don't know how to approach the problem I am having. Basically, the statement I am trying to make is: the fund's return is X standard distribution away from the mean. Normally, for a single fund, ...
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0answers
33 views

Return / yield of an ATM-Call Option on a zero coupon bond

The zero-coupon bond with unit face value and maturity S for a call option with maturity T and strike K is given by: The bond prices $P(t,T)$ and $P(t,S)$ $$\begin{aligned} ZBC(t,T,S,K) = & P(t,S) ...
2
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0answers
22 views

Use of second similar European Option as control variate to simulate a European option

I understand the idea and math behind the concept of control variate for the sake of variance reduction, but I struggle to apply it to option pricing. I need to simulate an European option of a stock ...
3
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1answer
147 views

derivation of general black-scholes formula

I would like to find a derivation for the Black-Scholes fomrula in the general case (i.e., where the volatility function $\sigma : [0,T] \to \mathbb{R}^+$ and the investment rate $r: [0,T] \to \mathbb{...
5
votes
1answer
344 views

Option pricing and mean reversion

In different books one can find a formula for option pricing when we assume that $\ln(S)$ follows a mean reversion process $$ dS_t/S_t=\kappa(\theta-\ln(S_t))dt+\sigma dZ$$ If we calculate an ...
3
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1answer
164 views

Finite Difference method in Matlab for SABR volatility model fails to provide correct option values

Currently, I'm trying to implement a Finite Difference (FD) method in Matlab for my thesis (Quantitative Finance). I implemented the FD method for Black-Scholes already and got correct results. ...
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1answer
108 views

Comparing historical to implied volatility

As title states, I am trying to compare historical to implied volatility of a stock. I approximate the single implied volatility (30 days forward) of the stock by first finding 2 series that ...
2
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1answer
58 views

Quantlib - model changes in option value on day of expiry

I'm trying to model option value changes during the progression of the last trading day before expiry. All option pricing Quantlib examples that I've seen work with day-level granularity. I'm ...
2
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1answer
79 views

Sigma moves - annualize return or no?

This might be a very simple dumb question. But when you look at a security's annualized volatility over a 3 year period, assuming the security has an annualized vol of 5% and the drawdown over three ...
2
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1answer
42 views

Optimal number of nodes for binomial lattice?

Let's suppose one is valuing a Euro call on a ZCB in a Black-Derman-Toy lattice. How many nodes/levels of discretization are optimal? Obviously too many creates computational issues and too few ...
2
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0answers
52 views

How should I interpret a forward rate?

Let $L(t, S, T)$ denote the forward rate from time S to T observed at time t, assuming t < S < T. A lot of modelling work is centered around this rate, but how is this rate useful? How are we ...
2
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1answer
153 views

Option Greeks' Formulas for Black & Scholes vs Black 76

I know Black76 uses forward prices instead of spot and that D1 calculation doesn't use the interest rate. Are there any other differences between the two? I'm calculating: theoretical value, delta, ...
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0answers
75 views

Heston Wrapper for QuantLib

As a follow up to my question here, I have written a (hopefully) easy to use Python 3 Wrapper around the excellent QuantLib library. My wrapper abstracts away all the QuantLib machinery under the hood ...
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0answers
49 views

Why is future price equal to $E^Q[S_T]$?

I understand that forward price is $k=E^{Q_T}[S_T]$. Why is future price equal to $E^Q[S_T]$ under the risk neutral measure?
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2answers
63 views

Calculating implied volatility from moneyness/volatility values for date

For an option expiring at a particular date I have Moneyness 0.4,0.7,0.85,0.95,1,1.05,1.15,1.3,2.5 Vol 0.105,0.075,0.045,0.045,0.202,0.045,0.045,0.075,0.085 ...
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0answers
27 views

What is incorrect with the following derivations of forward price?

We understand that the forward price of a stock S is $K=E^{Q_T}[S_T]$ where $E^{Q_T}$ denotes expectation under the T-forward measure. I have the following derivation that produces incorrect results, ...
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2answers
162 views

What is the numeraire for the real world measure $\mathbb{P}$?

We know the numeraires for the forward measure, the risk-neutral measure, etc. What is the numeraire for the real world measure $\mathbb{P}$?
2
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1answer
66 views

Why are vanilla OTC options are quoted in delta and vol?

Why do we quote options in delta bid-ask & volatility bid-ask & why not it is quoted in terms of option premium?
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1answer
77 views

Forward Skew in the Local Volatility Model

How does the local volatility model cause a forward skew? How is this different to the skew observed for future tenors in the vol surface?# Also how do LV models underestimate vol of vol?
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2answers
215 views

How does a Delta Hedged portfolio yield the Risk-free?

Here I'm considering the simple case of a dealer writing call options on a stock and hedging the short position with a "textbook" Delta Hedge, i.e. goes long on $N_c \times Delta$ stocks (where $N_c$ ...
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3answers
226 views

List of packages in R for options pricing?

What are the best packages in R or most comprehensive packages in R for option pricing and working with options? Thanks!
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1answer
84 views

Random Walk of N Correlated Assets

I am trying to value an option on N assets, say $S^1, S^2,..., S^N$ that expires in $\Delta T$ years using Monte Carlo simulation. I have read many sources that state I should use the following ...
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35 views
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0answers
26 views

Positive Heston model theta

Under the Heston model, is there a concrete example where the theta $\frac{\partial C}{\partial t}>0$ where $C$ is the price of a European call?