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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31 views

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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94 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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467 views

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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58 views

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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52 views

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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83 views

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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37 views

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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132 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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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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58 views

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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38 views

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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41 views

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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118 views

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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186 views

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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32 views

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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2answers
84 views

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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76 views

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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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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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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91 views

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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108 views

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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66 views

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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1answer
100 views

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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102 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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77 views

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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84 views

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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Delta of FX Options, Different Currency in Trading Book - Trading Interview Question

Having done stochastic analysis in university, together with tons of other math courses, do never prepare you for an actual interview in trading. Stumbled on what I believe might be an easy question, ...
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1answer
154 views

Monte Carlo: How to interpolate Dupire's Local Volatility

I am trying to price barrier options which can have daily or monthly observations. I first calibrated by Black vols into smooth SVI vols (with linear interpolation along time in variance) to obtain ...
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1answer
72 views

Calculate options prices based on given options and spread prices

Suppose you know the following information: Futures price on a stock is 66 70 strike straddle is trading at 27 50-60 put spread is trading at 2.5 50-60-70 put butterfly is trading at 0.2 Assume ...
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Backtesting Hedged Equity Portfolio with Options

I am trying to find some papers and methodologies on backtesting an Equity portfolio with broad-based index options as hedge. For example, take SPY and systematically hedge it with 9 months 30 delta ...
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1answer
91 views

Evaluating swaptions with negative interest rates

Does anyone know if it is possible to evaluate swaptions with negative interest rates with Quantlib? ...
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36 views

Is it true that interest rates options with different maturities are free of calendar arbitrage because of the different underlying rates dynamics?

The title says it all - is it true that European style interest rates options (lets say on LIBOR 3M for the sake of simplicity) with different maturities are free of calendar arbitrage because ...
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89 views

Black Scholes derivation: Why treat Delta as a constant?

In the derivation of the Black-Scholes equation, it is argued (e.g. in the original paper and in Hull) that $$dV(S_t, t)=(…)dt + \frac{\partial V}{\partial S} dS_t,$$ where $V(S_t, t)$ is the value at ...
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What is the TBA Option price convention and delta

I am wondering about price and delta about TBA options Use this trade example: One sell \$100 million ATM forward calls on 6.5% Fannie Maes for 24 ticks, and buy \$50 million ATM forward calls on ten-...
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85 views

Purpose of Vega Hedging

I am trying to understand the principle of vega hedging. When should a market maker vega hedge his position ? Let's suppose that a market maker delta and gamma hedge himself, and carries his position (...
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102 views

Optimize call option purchase

If it is predicted that the price of a stock will increase from P1 to between P2 and P3 in time T (assume the distribution of the price will be evenly distributed between the range of [P2, P3] at time ...
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177 views

Distribution of total delta of option portfolio

We know the delta of a portfolio of options is simply the sum of deltas of the individual options. But are there any additional known properties about the total delta (or other greeks) of a portfolio ...
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42 views

Difference between number of stocks and number of bonds: Predictable vs adapted

Let $\nu_k$ and $\eta_k$ denote the number of stocks and number of bonds in the portfolio. According to Schweizer, we need $\nu_k$ to be predictable and $\eta_k$ to be adapted. In the text, the ...
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1answer
134 views

No-arbitrage conditions on a caps/floors volatility surface

Suppose that one has a caps/floors volatility surface and wants to check whether this surface admits arbitrage. What is the theoretical and practical way to do it? Lets talk only about caps for ...
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42 views

Difference between Risk minimization and local risk minimization

According to the survey paper "A Guided Tour through Quadratic Hedging Approaches" by Schweizer the risk function is defined by $$R_t(\phi)=E[(C_T(\phi)-C_t(\phi))^2|\mathcal{F}_t]$$ When ...
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135 views

Why can’t delta’s be used to price double no touch options?

Here is the link to a MATLAB one touch option pricing calculator I used:OT I tried several inputs and I noticed that the one touch option price is approximately twice the delta of an equivalent ...

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