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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Dollar gamma formula and its derivation

I am seeing two formulas: $gamma = 0.5 * gamma * (stock price ^ 2) $gamma = gamma * (stock price ^ 2) Not sure where this 0.5 term is coming from. And also, what is the correct definition of ...
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The relationship btwn RV-IV and realized skew

In studying skew I've been advised to focus on understanding on components that affect it. One such component that's been recommended to me is the relationship btwn RV-IV and realized skew. ...
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How do we hedge option vega practically?

Suppose I’m a market maker, and I collect some spread buying an option due the flow I get. In this example, I must always quote. I want to hedge as much of the risk as possible over the lifetime of ...
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local volatility not reasonable

We are going to generate synthetic option prices using a Heston model, i.e., $$ \begin{gather*} dS_t = \sqrt{v_t} S_t dZ_t,\\ dv_t = \lambda (\mu - v_t) d_t + \eta \sqrt{v_t} dW_t, \end{gather*} $$ ...
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Should you compute the greeks on realized or implied volatility?

I am reading Trading Volatility by Collin Bennett and he says that you should compute the Greeks using realized volatility rather than implied volatility? Is this actually true? As far as I know the ...
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Hedging rates exposure in an FX options book

Fx options have exposure to the interest rates in the domestic and foreign currency. This risk can be hedged using currency forwards. In an ideal world, I suppose the best way would be to hold ...
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Pricing binary options under volatility smile

I was asked to show that the price of a digital/binary option $D$ while a volatility smile $\sigma(K)$ is present is given by $$D= \exp(-rT)( \Phi(d_2) - K \sqrt{T} \phi(d_2) \sigma ' (K))$$ Where $\...
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Data for Japanese options

I'm working on an academic project that requires data for options tracking ~300 large Japanese stocks between 2010$-$2020. The standard data source I've seen quoted in academic papers is OptionMetrics,...
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How do trading platforms estimate options pricing P&L graphs?

Using the profit/loss calculator for equity option strategies of a trading platform, it displays estimated P&L curves for some date in the future and across the prices of the underlying with a ...
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How can you trade steepness by combining cash and different futures?

When you believe an asset is going to go one direction, and also have an idea about how steep that movement will be vs time, I think there are ways to trade this idea by combining cash and futures for ...
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Implied volatilities for different options that track the same stock

I have a somewhat basic question regarding option prices. Suppose we have an underlying stock and two different options (that have different strike prices, maturities, etc.) that track this stock. ...
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You are long a hedged ATM SPX Call and the market moves down. Do you gain or lose in volatility terms?

The shape of the volatility curve in index options trading typically shows that the 'just' OTM Calls (ITM Puts) options have the lowest implied volatility. If you are long an ATM Call and the market ...
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Calibrating Heston model using implied volatilities

I'm trying to understand how the authers of a paper calibrated their model. We got data on European type options on the S&P500-index period from early 2005 to mid-2009. We have daily data on ...
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Where does the term $\gamma$ come from when moving from measure $\mathbb Q^{N}$ to $\mathbb Q^{M}$?

Consider two measures $\mathbb Q^{M}$ and $\mathbb Q^{N}$, as well as the two numéraires $M$ and $N$, furthermore assume that $X\frac{N}{M}$ is a $\mathbb Q^{M}$-martingale. Furthermore, the ...
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How am I supposed to understand the following statement on the convexity adjusted rate

Given, a numéraire $(N(t))_{0\leq t \leq T}$ and an index $(X(t))_{0\leq t\leq T}$ that is a $\mathbb Q^{N}$-martingale, we consider the natural payoff $V_{N}(T)$, where it pays $$V_{N}(T):=X(T)N(T) \...
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Extrinsic value larger than strike distance [closed]

Let a stock trade at 50\$. Would it be possible for a call at the 55\$ Strike to trade a a price greater than 5$? I'm pretty sure that there has to be an arbitrage opportunity, I'm just not seeing it. ...
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Finding the distribution of $I(T_{1},T_{n})$ under an appropriate measure if the forwards are lognormal? [duplicate]

My question follows beneath the "lengthy" setting I describe: Given a tenor discretization $0 = T_{0}< ... < T_{n} =T$, and under the assumption that under $\mathbb P$, for all $i = 1,....
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Easier way than using QuantLib to compute the price and Greeks of a vanilla European option?

I'm using the following to compute the price and Greeks a vanilla European option: ...
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194 views

Early exercising American put options

I have found a proof that an American put option without dividend will never be exercised early. However, I suspect that that is not true, so there should be a mistake in the proof. The proof is as ...
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Why does the diffusion term remain the same when we change pricing measure?

Consider some Itô process $dS(t)=\mu(t)dt+\sigma(t)dW^{\mathbb P}_{t}$ under the measure $\mathbb P$, where $W^{\mathbb P}$ is a $\mathbb P$-Brownian motion In plenty of interest rate examples, I have ...
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implied vol by Delta

I am looking at some data that is Delta 10, Delta 30, etc for an index option CDX IG. I know the meaning of Delta, as a sensitivity of the price move with respect $1 move in the underlying index. What ...
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How To Construct A Volatility Spread Position?

Is there a simple way to spread the volatility of one product against another? By simple I mean one trade executed on each leg rather than constant delta hedging. I can see a lot of opportunity for ...
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Why would valuation for a swap be the same on the backward and forward rate but not a caplet

Consider for time discretization $0 = T_{0} < T_{1} <... < S < T < T_{n}$, and the corresponding forward rates and backward rate: $\text{Forward rate: }L(S,T;t)$ $\text{Backward Rate: }...
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How to combine compound calls and puts such as to have a guaranteed fixed payoff at expiration?

Let there be 2 European vanilla options: Call; Put; Both options expire at time T2 > T1 > t=0. We also have 4 additional options available to us: Compound call on call; Compound call on put; ...
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168 views

Backtesting Option Strategies with IV Data Only

I’ve tried to find a good answer for this but had no luck so I’m bringing it here: potentially beginner question, but how much accuracy would I be sacrificing by backtesting an options strategy with ...
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Pricing asian options with Monte Carlo and brownian bridge

I am trying to price arithmetic asian options using Monte Carlo method and a brownian bridge construction. My code does not seem right as the price with a geometric conditioning gives me a price of 5....
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Is there a closed form formula for the value of a European Put KO/KI?

Was able to find closed form formula for single barrier options KO OR KI. However I haven't found that for a double barrier option. I am looking for a put down & in KI, up and out KO, where: H(KI) ...
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US stock options data with resolution less 1 min

I'm looking for data (with a delay, but ideally with a real-time option) of the prices of options on US stocks with resolution less 1 min (1-5 sec). With a reasonable price for a pet project - I have ...
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1 vote
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107 views

How does $(d_2/\sigma) = (1-d_1)$ while deriving the Vanna Formula from BSM? [closed]

Just realized there was a quant finance board, so I figured I'd post it here instead. I'm trying to derive Vanna from the Black-Scholes Model (BSM) equation, but had a hook up on one of the ...
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Why is the parity graph in Natenberg shifted up?

In chapter 4 of Natenberg's "Option and Volatility and pricing", he discusses how to draw parity graphs for option positions. These are defined as a plot of the intrinsic value of the ...
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Portfolio optimization and decorrelating short term option payoffs

I'm looking to analyse whether one is better off selling OTM weekly covered calls, and rolling them, compared to selling monthly covered calls. There are some expectations on the yield so I cannot go ...
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Assymetric Rate Distribution

The pandemic has disavowed any notion of nominal rate distributions to being truncated at 0%. However, if Central Banks at Debtor nations are conflicted in that they are incented to suppress interest ...
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How to create a profit target order in TWS against my option position?

I am a beginner in trading options and in using TWS with options. I have an iron condor position in TSLA. I want to create a limit order to act as a profit target for my position. I am able to create ...
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Explanation of barrier option code

I'm wondering if anyone can explain the code behind the pricing of barrier options (in particular the def(up_and_out_call) part. I'm finding the loop inside of a loop concept quite confusing. Thanks. <...
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at what frequency do option market makers delta hedge

Could someone with option market making experience tell me usually at what frequency do the major option market makers delta-hedge their positions (say for US single stocks or equity indices)? ...
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How does an Options Market Maker (OMM) deal with an asymmetric inventory?

Let us use an example of a market maker quoting the ATM straddle. Under Black-Scholes: S = 100 K = 100 DTE = 3 IV: 20 r = 0 q = 0 No rates or dividends for ...
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How to find the risk neutral valuation of $P(T_{1})$ und the measure $\mathbb Q^{P(T_{2})}$

How do I find the risk neutral valuation of $P(T_{1})$ und the measure $\mathbb Q^{P(T_{2})}$, where $P(T_{1})$ and $P(T_{2})$ refer to the $T_{1}$ and $T_{2}$ zero coupon bond with $0 < T_{1} < ...
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What adjustments need to be made before a Monte-Carlo simulation can be applied for the exotic option $(L_{\text{domestic}}-L_{\text{foreign}})^{+}$

I just want to reassure myself that I understand why Monte-Carlo is the appropriate tool in computing the fair value prices for different options. Let's say we have a Tenor discretization $T_{0}=0<...
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Gamma PnL when hedging with implied volatility - where is the mark to market PnL?

It is well known that hedging with implied volatility involves a PnL: $0.5*(σ^{2}_r−σ^{2}_i)S^{2}*Γ_{i}dt$ In the Wilmott paper (http://web.math.ku.dk/~rolf/Wilmott_WhichFreeLunch.pdf), they imply ...
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Understanding the expected value of the average

I've been looking into Asian Options pricing. Part of the process is about looking for the expected value of the average of a time series undergoing e.g. geometric brownian motion. I came across this ...
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7 votes
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118 views

Implied vol bounded if and only if instantaneous vol bounded

I'd like to show that in diffusion models IV is bounded iff instantaneous vol is bounded if there is to be no arbitrage. So, assume a model under the pricing measure of the form $$ dS_u = \sigma_u S_u ...
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1 vote
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Issues with calculating IV with options bar data

I am currently working with some options OHLC data (30 minute bars) from IBKR for a range of strike prices, maturities and for both calls/puts. For each bar, I am trying to back out the IV (crudely ...
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Under put call parity shouldnt the implied volatility for call and put for same strike and maturity be the same?

If all of the other inputs into black scholes (divs/rates/time to maturity/strick/current price/etc) are all the same between two pairs of calls/put contracts on the same security, shouldn't the ...
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In FX markets, option can be expressed as either call or put. Explain

For example, if option contract has condition: $AUDUSD = 0.8$ at the maturity date, and current exchange rate is $1 AUD = 0.75 USD$. For this option, it could be considered a call option on $USD$, and ...
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Valuation of chooser options

The below formula for valuation of chooser options from Hull's book is not making sense to me. Why do we use call value at time T=0 while we use put value using t=0 call value and discount strike and ...
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2 votes
1 answer
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Confusion with the equity option skew

In general out of the money (OTM) equity options have higher implied volatility (IV) than at the money (ATM) options. So assuming we have two put options (5% OTM and 10% OTM). Skew reveals that 10% ...
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Is there a financial instrument that is exposed to the change in growth of an asset over time?

Is there a financial instrument that is exposed to the rate of change of the value of a specific asset? If I believe a stock price will continue to grow in the future, but grow more slowly than in the ...
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2 votes
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110 views

Numerical scheme for this HJB equation

Without dwelling on details on how to obtain the HJB equation for this problem, I would like to know if the scheme I wrote for solving it numerically is viable or did I miss something. I need to solve ...
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Determine Strikes on Option Chain

Does anyone know how to determine option strikes on an option chain are determined for a specific stock? I have been searching online and can't seem to figure out how/why the specific strike are set. ...
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Volatility of American vs European Stock option return

Let's say that I hold an American Call Option (ACO) and an European Call Option (ECO) in my portfolio on the same underlying, with same strike price and same maturity date. Given that I hold both ...
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