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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Duan (1995) GARCH Option Pricing Model with MATLAB

I found a MATLAB code online (on Volopta) that replicates the option pricing model proposed by Duan in his paper "The GARCH Option Pricing Model". However, the parameters estimated in the file do not ...
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25 views

What is the name of these digital basket options?

Consider a basket of correlated assets $(S_1(t),\ldots, S_N(t))$, as well as a vector of strike prices $(K_1,\ldots,K_N)$, and let's look at the following European payoff types: An option that pays 1€...
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103 views

Options Market Making Used Implied Volatility Surface

Suppose you are a market maker with a model that is producing an implied volatility surface for you. Suppose you quote bid/ask prices (vols) around the prices given by your implied vol surface. In ...
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Finding payoff and profit

Consider a European call option on a Microsoft stock with an exercise price of 20 dollars. Assume that the expiration date is in four months and the price of the option is 5 dollars. The current stock ...
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143 views

VXX Put pricing

Last week at Friday's close, the Dec 14 37.5 Put options were selling for \$.68 with VXX at \$40.29. This week at Friday's close, the Dec 21 37.5 Put options were selling for \$.38 with VXX at \$40.50....
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139 views

Implied volatility equality for deep in/out-of-the-money put and call

Someone posed the following question. Given a strike $K$ and the stock price $S$ and the same maturity are the implied volatilities of the call and put with these same parameters equal for $|S-K|\gg0$...
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62 views

Why and how is Implied volatility directly related to stock price but inversely related to strike price?

I know that in equity markets there is a volatility smirk which results in higher IV for lower strike price options because of crashophobia and leverage related factors but I can't wrap my head around ...
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Why would a buyer buy a Warrant vs an Option, both having the same economics

Assume you have a Warrant and an Option both with the same economics i.e strike, expiry, type etc. Also assume that the Warrant has been issued by a high grade reputed issuer (i.e there is a almost a ...
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399 views

Why risk neutral probabilities should be strictly greater than zero for no arbitrage condition?

I was recently told by a colleague that the risk neutral probabilities should ALWAYS be greater than zero to have a no arbitrage condition. Intuitively, we know probabilities cannot be < 0, but how ...
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1k views

Why a Target Redemption Forward cannot be used as hedging instrument?

A Target Redemption Forward (TARF) allows you to buy or sell foreign currency at an agreed “Enhanced Rate” for a number of expiry dates. But why can't a Target Redemption Forward (TARF) be used as a ...
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Procedure of model calibration

Say that your end goal is to price an equity exotic derivative under both Heston and the local volatility models (Black Scholes model with vola dependent on strike and underlying level). Do the ...
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Optimal Hedging of Options - asymmetry between long and short vol positions

Going over Zakamouline's Approximation method for optimal delta hedging of options, it is claimed that the result remains valid for both buying options (long vol positions) or selling options (short ...
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1answer
55 views

Can someone provide a good definitive explanation for rho in relation to option risks?

I have a pretty good understanding of option risks except for one thing, rho. Unfortunately, interest rates tend to have a small effect on option prices, and thus most literature tend to just gloss ...
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44 views

SPX options strike bracket

By what rule does the CBOE determine the available strikes for puts and calls on the SPX? The contract specification (http://www.cboe.com/products/stock-index-options-spx-rut-msci-ftse/s-p-500-index-...
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43 views

If 10s20s steepener have equal DV01 weighting on each swap then why does convexity play a role in MtM

Receiver Swap 10yrs Notional: 1,000,000 DV01: +1,300 Tenor: 10yrs Rate: 4% Payer Swap 20yrs Notional: 500,000 DV01: -1,300 Tenor: 20yrs Rate: 5% Looking at this fictitious example, I want to ...
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190 views

Why does expected price of OTM option not equal to BS price?

If I assume that stock returns follow normal distribution with drift = 0% and S.D. = 10%. In the long, if I keep investing in this stock for a year with the same capital every year for a consecutive ...
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73 views

Why is the value of the Brownian motion bounded by the maximum value of this square difference?

This comes from Taleb and Madeka's paper (https://www.academia.edu/39998351/All_Roads_Lead_to_Quantitative_Finance_Response_to_Clayton_?auto=download) regarding arbitrage restrictions on binary ...
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233 views

What is the industry standard pricing model for CME-traded Eurodollar future (American) options?

The CME-traded Eurodollar futures option is an American option. What is the industry standard pricing model for this product? Does the industry practice to treat CME-traded Eurodollar futures ...
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8k views

When does delta hedging result in more risk?

A question from an interview book: When can hedging an options position make you take on more risk? The answer provided is the following: Hedging can increase your risk if you are forced to ...
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390 views

Why does buying future options require margin?

An option is the right, but not the privilege, to trade an underlying at the strike price. Buying a stock option doesn't require any margin - I've just tested this with InteractiveBrokers, trying to ...
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55 views

In literature, is IV constantly adjusted during option delta hedging?

In a lot of literature, they like to compare the performance of buying an option, and then delta hedging either at that options implied volatility (IV) or the true future volatility. This is under ...
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theoretical reason for which we can use monte carlo simulation for option pricing

The classic way to price an option is solving either analitically or numerically the associated PDE subject to the terminal and boundary conditions. An alternative approach is to use monte carlo ...
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4answers
283 views

How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...
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2answers
401 views

What are some beginner quantitative option trading strategies?

I'm new to quantitative trading, with good knowledge in finance and coding (mainly Python, Java, R, etc). I would like to know if there are any basic quantitative option trading strategies that can ...
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Trading with S&P 500 options

Could someone help me who has experience with trading S&P 500 options? I am curious about any liquidity trends (if OTM, ATM, ITM are the most liquid, and with what kind of maturity), and the ...
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Is it possible to price a double barrier option which one barrier is monitored continuously while another barrier discretely without using MCS?

I am thinking about pricing a down-and-in and up-and-out double barrier put option under Black-Scholes assumption. The upper barrier is monitored continuously and the lower barrier is monitored ...
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Delta Neutral / Gamma Neutral Positions

I've been trying to find out more about options positions which are both delta neutral and gamma neutral--created with some kind of calendar spread. Supposedly, such a trade will be perfectly hedged ...
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285 views

How to hedge two currency positions

Having two spot currency positions, short EUR/USD long GBP/USD We are looking for a way to diminish the risk of the spread going against us. The basic idea is ...
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446 views

Leveraged Permanent Portfolio Using ITM Call Options

The permanent portfolio proposed by Harry Browne has had an excellent track record since the 1970's. It is able to compound at roughly 8% annually with a Sharpe ratio around 0.7. The permanent ...
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Vol surface fitting to options on commodity futures

Trying to fit variants of SVI (Zeliade method, SSVI etc) to options on futures price data. One of the core ideas of the SVI parameterization is the absence of calendar spread arbitrage. I think the ...
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Hedging Strategies involving Forwards and Options [closed]

"An investor or business with long exposure to an asset can hedge exposure by either entering into a short futures contract or by buying a put option. An investor or business with a short exposure to ...
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Hedging an option on a non-traded asset in BS world

I have given the following task given. Suppose you are in a Black-Scholes World where you have the standard assets $$ dS_t = \mu S_t dt + \sigma S_t dW_t $$ $$ dB_t = r B_t dt $$ and now you also ...
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Gamma PnL Formula and Break-Even volatility

When we derive the P&L of a delta hedged option we obtain: $$ \text{P&L}=\dfrac{1}{2}\Gamma(\delta S)^{2}-\theta\delta t $$ and setting equal to zero and rearranging we obtain: $$ \dfrac{1}{...
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Why does implied volatility show an inverse relation with strike price when examining option chains?

When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts. As a current ...
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174 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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How to calculate the risk neutral probability of the underlying price always exceeding the lower barrier K during a given time?

I'm trying to price the autocallable structured products by a probability approach proposed in the following paper: Modeling autocallable structured products, by Geng Deng, Joshua Mallett, Craig ...
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144 views

How is FX cross rates options are priced?

Say I have market for EUR/USD and also USD/CAD, how would EUR/CAD would be priced and hedged in practice? What are good papers/book chapters to read on that? (Assuming basic knowledge already on ...
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Banks' use of written interest rate options

I study US commercial banks data. I look at the notional amounts of their different OTC interest rate derivatives for the recent years. When I look at non-dealer banks (i.e. end-users), I find that ...
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Numerical Solutions to PDEs with Financial Applications

I am reading a paper by Richard White, Opengamma named Numerical Solutions to PDEs with Financial Applications. There is an implementation codes as stated in paper hosted at https://opengamma.com/...
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274 views

Exercise Probabilities Vanilla Cap/Foor

When looking at the discounted pay-off formulas of a vanilla caplet and a vanilla floorlet $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_k-r_{cap},0)$ $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_{floor}-...
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Why do coefficients flip after the including a lag in the optimisation? implied volatility/skewness/ivspreads

I'm hoping some of you guys can help me out. I am applying the paramametric portfolio optimisation of Brandt, Michael W., Pedro Santa-Clara, and Rossen Valkanov. in which the weights on specific ...
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A simple formula for calculating implied volatility?

We all know if you back out of the Black Scholes option pricing model you can derive what the option is "implying" about the underlyings future expected volatility. Is there a simple, closed form, ...
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1answer
47 views

How to price a phoenix and snowball type autocallable options?

I'm currently studying the pricing of autocallable options, especially snowball (accumalated coupon) and phoenix (accumlated coupon, but the coupon may also be autocalled if the underlying price ...
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17k views

What is a Heat Rate Option?

I tried a search with google but I can't find a clear definition of what a Heat Rate Option is. I would appreciate if someone could explain to me what this type of option is. My understanding is ...
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Does convexity in the IV space means convexity in the price space?

Let's assume that we only look at OTM options to construct a Risk Neutral Density (RND). As the RND is the second derivative of the price of the option with respect to the strike, we would expect ...
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63 views

OTC Derivatives Moneyness Conventions

When looking at the OTC Derivatives market, is there a standard moneyness convention that is applied? And if so, what is that bucketed approach? For example: 90%-110% for ATM, 70%-90%, 110%-130%, etc.....
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276 views

Basic Replication of European Call Option

I am looking at the very basics of replicating an option with a portfolio of risky and risk free assets. As such we can define a portfolio of $x$ no. of shares, $y$ bonds & $z$ options at time $(T)...
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Settlement of currency options

wanted to understand the market action done to settle a call option. Let's say I entered into a export seagull for eurusd and on the date of expiry my sell call gets exercised. Assuming that my sell ...
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1answer
103 views

How does the volatility skew/smile relate to hedging/trading vanilla contracts?

I know that obtaining and calibrating the smile is important in the hedging and trading of exotics since we use vanillas to hedge and price exotics. How is the smile important in the hedging and ...