Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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1answer
55 views

Finding the extrinsic value of an option with conditions

Background: Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant. Let's also assume, that the correlation ...
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88 views

How does the Black Scholes Model Incorporate Log Prices Into Model?

I am still not understanding the link between log prices and how that is incorporated into the BS model. I understand why log(S) is assumed because it makes math easier and it prevents ending prices ...
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53 views

Log Contract payoff function

I can’t get where Dr. Rouah gets payoff function of log contract. Could you please take a look at that? https://frouah.com/finance%20notes/Variance%20Swap.pdf It’s on page 2, section 3. I couldn’t ...
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21 views

How to calculate a prepayment penalty on a mortgage

I have issued 2 mortgages...one with an option to prepay the loan, the other without that option. I want an objective way of calculating the extra interest rate (compared to the second) and ...
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20 views

Pricing a transfer option for oil

Need some input in how to attack this problem. Given are 8 timeseries: UK Oil price, Delivery Quarter 1 2020 UK Oil price, Delivery Quarter 2 2020 UK Oil price, Delivery Quarter 3 2020 UK Oil price, ...
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34 views

Using Non-Risk Neutral (Risk Natural) Parameters to Price Options?

Please correct me if any of my following statements are false. My understanding as to why we use Risk Neutral Analysis is that it makes life easy, and ultimately, allows use to come to a closed form ...
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44 views

How can I manually calculate the VAR of a call and put portfolio?

How would I solve the following question? Im unsure how to estimate the stock price using MCS.
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38 views

Understanding delta based strike selection in an Iron Condor

I am reading a small book on the proper use of Iron Condors (link). I do not use these strategies as I have had a very hard time being profitable on them. This book mentions some strategies to ...
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1answer
351 views

How could one trade volatility skew if you think it's too flat or steep?

We all know that you can trade on a forecast of volatility by dynamically hedging, but I'm wondering if there's a similar technique where in you can trade the skew specifically? Let's say you travel ...
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66 views

Kirk Spread Approximation, Greeks by Finite Difference

I am using finite difference on Kirk's Approximation for Spread Options to estimate greeks of the Spread Option. Now this is creating an problem in the estimation of gamma. For at the money options (...
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49 views

Negative vega on IR swaptions mid curve

Why do IR bermudan options have negative vega on midcurve? Does it have something to do with mean reversion and a way of lower the price vs market prices?
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2answers
203 views

Factor model and trading strategy in options market

We all know that there are many factor models (CAPM, Fama-French 3...) and trading strategies (momentum trading...) in equity market. I wonder whether there are any analogous factor model and momentum ...
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33 views

What adjustments need to be made to Heston model to price futures options? [duplicate]

My understanding for the Black Scholes model is that a few adjustments need to be made so that the BS model can be used to price futures. Hence the Black-76 model. What adjustments, if any, do we ...
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153 views

Early Exercise Options and Coin Flipping

This problem was presented in an interview, and I know I got it roughly correct. But I am still not entirely understanding the early exercise component of it: Say I am advertising a game where I ...
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74 views

Is there an arbitrage free option model that treats volatility as a deterministic function of strike?

I am trying to get a good understanding of the different models out there, and thus be able to study hedging errors, and strengths and weaknesses. My understanding of the Local Volatility model in ...
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44 views

Put call symmetry of put

I hope this is a simple question but I just wanted to get confirmation and also the intuition behind it. I know the put call symmetry and I often see it expressed as: Call(S, K) = Put(K, S) = K/S Put(...
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1answer
68 views

Deriving the risk neutral probability with the arrow debreu Price vector

today I had an oral exam about Stochastic Finance. With one of the questions I was pretty helpless. We were talking option pricing in a scenario where we have Portfolio with n-assets and k-states. But ...
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1k views

FX Option strikes from ATM, RR, BF quotes

I am trying to replicate the results in Consistent Pricing of FX Options, A. Castagna and F. Mercurio. However, when I calculate the strike prices for 25-delta put and call and ATM I cannot get the ...
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41 views

Free Call Option [duplicate]

Suppose we follow the assumptions of the Black-Scholes Model, including unlimited borrowing, continuous prices, and frictionless markets. For simplicity assume the risk-free rate is 0. In this world, ...
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1answer
101 views

What's the logic behind binomial model ups and downs?

I want to understand what is the underlying logic in the calculation of u and d in a binomial model. $$ u = \exp\Bigl(\sigma \sqrt{\Delta t} \Bigr), \quad d = \exp\Bigl(-\sigma \sqrt{\Delta t} \Bigr)...
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83 views

Solving for Implied Volatility Vega gets stuck at 0 (Python)

So my goal is to calculate option greeks with as few manual inputs as possible. I managed to get the IV for at the money options but then when I try further OTM strikes my results get completely ...
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2answers
2k views

Call and Put Prices Equal at Forward Price - Why?

Consider a European call and put with values $C_t$ and $P_t$, respectively, under the Black-Scholes model. By put-call parity, $$ C_t - P_t = S_t - Ke^{-r(T-t)} $$ for expiration time $T$. Note if $...
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2answers
150 views

What is “Lambda” in Heston's original paper on stochastic volatility models?

In his paper (link), he has the equations: b1 = k + ƛ - (ρ * σ) b2 = k + ƛ k is the rate of mean reversion, ρ is the correlation between the two Wiener processes, σ is vol of vol, what is ƛ? ...
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34 views

Binomial model option

An American call option with exercise price $K = 90$ written on an asset where the asset prices in dollars are given below, the interest rate per period is zero, and a dividend of $5$ is paid between ...
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1answer
91 views

Why Can I not estimate a CVAR from Heston Model

I fit the parameters of Heston model, using option data for SPX. Now I have the process S and P 500 is expected to follow. I make 100,000 simulations of this process and then calculate the expected ...
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1answer
119 views

Is there a simple, intuitive derivation (using Taylor series) of the following approximation to Vega-weighted Implied Volatility?

The approximation is: $$\sigma \approx \frac{\sum V_j\sigma_j}{\sum V_j}$$ Background information from the first answer to this post: "Say that you have a portfolio of options with prices $P_j$. ...
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1answer
87 views

Derivatives Trading Jargon

Could you please help to understand trading jargon in this tweet. Thanks in advance. For non twitter users: Bookie pushing 5-delta (strike of 8) 2 month TRY puts. 0.6%
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Where to Find Foreign Countries Index Option Data

OptionMetrics database contains option data for several US indexes (SP500, SP100...). But I don't see any option data for foreign indexes. Is there a place from which I could get/purchase the options ...
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109 views

Geometric Brownian Motion with Dividends

I am working on a problem and had a quick question. I understand that for Geometric Brownian Motion we use the formula: $$X_{t_n} = X_{t_{n-1}} + \mu X_{t_{n-1}} \Delta t + \sigma X_{t_{n-1}} \...
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53 views

Risk-Neutral Pricing with Regime Switching

As the title suggests, I am currently trying to implement a dual regime-switching options pricing model. In its simplest form, I am fitting a risk-neutral GARCH(1,1) to a crash and normal regime. ...
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1answer
538 views

Differences between Snowball, KIKO and TRF derivatives?

Can you explain what are some similarities and differences between snowball, KIKO (knock in knock out) and TRF (target redemption forward) derivatives?
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147 views

Pricing in the Heston Model

The dynamics of the Heston Model is \begin{align*} \frac{dS}{S} & = \lambda \sqrt{\nu} d W^S \\[0.5em] d \nu & = k (1- \nu )dt + \epsilon \sqrt{\nu} dW^\sigma \end{align*} where $\lambda$...
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1answer
86 views

Static hedge for up-and-out Digital Call

I am trying to come up with a static hedge for a Digital Call with strike K that knocks out when price > barrier H. I know it will involve non-knockout digital calls with strike K and strike H but I ...
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1answer
60 views

Asian Options Vs Bermudan Options

Which of these options are more popular in practice/used in industry? And where exactly are they used? Also, I have been searching for listed Asian and Bermudan options, for volume data etc, but have ...
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1answer
75 views

Looking for a Book

I hope everyone is well. While I was looking for derivations of Greeks I came across part of a book. Could you help me to find its name please ? Here is the link: http://centerforpbbefr.rutgers.edu/...
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53 views

Poisson parameter in Merton's Jump-Diffusion Model to price call option

I've been taught the following European call valuation formula under jump-diffusion model: \begin{equation} price = E[e^{-rT}max(S_T-K,0)] =\sum_{j = 0}^\infty e^{-rT}P_j(\lambda)E[max(S_T-K,0)|J=j] \...
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111 views

Numerical simulation of Heston model

I am trying to simulate on Python random paths for a general asset price as described by the Heston model: \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &...
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1answer
46 views

Why is there no parameter for the estimated economic growth of a company in the option price model

Can someone explain me why the economic growth of a company is irrelevant in determining the option price. Especially for options with a long maturity e.g. 5 years it seems to me that for a high ...
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1answer
91 views

Black Scholes- Options and OIS

I have 2 questions. In the Black Scholes formula for currency options, where does forward premium come in? Volatility will be a historic parameter, so which component considers fwd premia. Typically,...
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1answer
56 views

How to understand firm option expiration cycle?

Here I am trying to understand the firm option expiration cycle: When I read Investopedia, it says: Most of stock options are on one of three expiration cycles, which consists of one month per ...
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1answer
230 views

Where can I get Currency options historical data?

where can I get historical data for currency options? For most part, google gives me links to binary options and other shady webpages.
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107 views

Fitting a forecasting S&P500 roll volatilities

I have a time series of S&P500 prices, for which I have calculated log-returns and roll-volatility. My goal is to forecast daily realized volatility and test a straddle strategy based on it (I ...
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146 views

Why historical volatility is calculated as N-days annualized?

Annualized historical volatility is always calculate with 10-, 20- days time window. I don't quite understand. Compare with annualized historical return, annualized historical return is never ...
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3answers
2k views

Which volatilities should I use for Quanto Options?

Quanto options pricing formula, as described in this paper is a function of two volatilities: one from the underlying asset and another from the exchange rate. How can I read the "right" volatilies ...
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1answer
90 views

Inherent volatility of selling longterm options and buying short term options

A two-month option has an implied vol of 60%, the corresponding 2-year option has an implied vol of 34%. You buy the short terms and sell the long terms. What is the inherent volatility of the total ...
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5answers
334 views

Heston Model Integration Oscillations

Is there a way to reduce oscillations for the numerical integration when evaluating the Heston model. I am pricing a series of 5000 options scattered over the Heston model parameter space and I find ...
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63 views

Pricing an exotic with barrier at discrete times

How would you price the following option on underlying $S$ without dividends? Time to maturity of option $\tau = 12$ months Option has a strike $K > 0$ and constant barrier $B > 0$. $t_0$ is ...
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173 views

Fitting Gatheral's SVI model

I was considering using Gatheral's formula for fitting option skew. In the specific (commodity) market that I am concerned with, the underlying is ca. at 50, and typically 5 integer strikes left and ...
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1answer
70 views

Call Option Overvalued and put-call parity [closed]

I have a question regarding if a Call option is overvalued compared to the call price and how you can benefit from the Arbitrage opportunity. My thoughts are as follows: Step 1: Short the call ...
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223 views

Higher Order Greeks

In studying options pricing a while back, I had learned of the higher order sensitivities of of Speed and Color. Speed was the rate at which the gamma changes with the underlying. Color is a ...