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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29 views

Calculate the size of the up move from volatility for Binomial model

I'm given a European Put option, current and exercise prices, $p$ and $P$ and stock volatility $q$. What is the way of finding the size of the up move from the problem?
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39 views

Option pricing with risk-neutral approach

Problem Given $Y_t$ price of a stock (no-dividents), and a derivative paying $Y_T^2$ at maturity $T$, evaluate the price of the instrument now using risk-neutral approach and check that it satisfies ...
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38 views

Compute call option price given two stock price scenarios? [closed]

I was asked the below question, but wonder if enough information was given: For an AAPL European call option expiring in 1 year, strike price is $159.60 AAPL is now \$144.00. In one year, it can go ...
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30 views

Easy, but doubts - Annualize daily turnover

I am fairly certain I am correct but I just want to double-check on portfolio turnover calculation. I need to annualize the daily turnover rate. To calculate, the daily turnover, I am using the ...
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Put call parity without dividend confusion [closed]

If the underlying asset pays no dividend, then CE(t,K)- PE(t,K) = S(t) - Ke-r(T-t) Proof for the above formula: First, we have Portfolio 1. At time t, long 1 call option and short 1 put option, so ...
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34 views

Construct an arbitrage portfolio using combination of European call options [closed]

Suppose that the continuous compounding rate is r = 0.05 and the maturity time T=1. How can I construct a portfolio using some of the European call options below and the bank account to find an ...
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54 views

Prove that value of Vanilla put option increases when time to maturity increases [closed]

Given two vanilla put options with the same strike price K but different maturity dates T'<T. If the interest rate r = 0 between T' and T, how can I prove that P(t, T') < P(t, T) ?
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104 views

Greeks of portfolio in response to underlying price change

I'm trying to wrap my head around Greeks, and I'm getting a little bit confused. For example, let's say my portfolio holds a long 5 month ATM call with strike \$20, and short 2 month OTM call with ...
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46 views

CDS Option Pricing (Missing Index Factor)

I've read the OpenGamma paper https://quant.opengamma.io/CDS-Options-OpenGamma.pdf on CDS Options, and noticed a small discrepancy. So I wanted to double-check my understanding. In Section 6.4 the ...
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143 views

Can gamma of an option be greater than its delta?

I have a currency pair usdinr put option with strike price at 73.5 INR, risk free rate 0, underlying price of 75.4025, days to expiry is 15 and iv is 5.9%. Delta of this option is -0.019 and gamma is ...
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66 views

What is the greatest theoretical delta value?

In a few options positions I'm currently holding I noticed delta values of ~0.6 while gamma is ~1.0 which surprised me as I thought delta can never be greater than 1 - meaning for every 1\$ move in ...
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25 views

Arithmetic Asian options on two commodities

I am pricing a November-December Asian option on steel via Monte Carlo simulation. I intend to simulate daily prices for the Nov contract from today through end of November, and from today through end ...
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47 views

Optimizing Options Portfolio

I’m working on a model which creates a portfolio of options. The model has an alpha from an options trade for 1 period using several different underlying stocks. Would Mean Variance optimization still ...
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22 views

Exposure calculation - modeling/Valuation/Validation [closed]

Hey I would like to know a bit more about calculating exposure. We need to simulate risk factors such as interest rates or FX rate using different models (what are the most popular for each type of ...
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123 views

Why is call option value same as portfolio value at all times in Black Scholes model?

Following is a part of the text from Steven Shreve Stochastic Calculus for Finance II, for pricing the European Option in Black Scholes model. The argument is that today I start by selling a European ...
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251 views

Why are options studied separately from a portfolio of stocks and bonds?

I have just started studying finance and stochastic calculus so apologies if this question is too naive. I was first introduced to stocks and bonds as risk and riskless investment assets. Then a new ...
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Cash less exercise and redemption feature in SPAC warrants

Public and private warrants of a SPAC post merger (Initial Business Combination or IBC) are often very similar. Notable differences are 1) cashless exercise of the private warrants and 2) redemption ...
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41 views

Why doesn't the value of an in-the-money option increase approaching expiration? [closed]

I know it is a pretty basic question and I can get this result with BS, however I don't understand it conceptually. As the time approaches maturity, it is less likely to end out of the money, so I ...
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16 views

What are the different payments in a callable spread option? how is it structured

I encountered a product that's called CSO (Callable Spread Option). I would like to understand how this product works and how the payments are done in both ways? what about the callability of the ...
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39 views

What is the cause of this option chain anomaly?

LAST CHG BID   ASK VOL OPEN INT. STRIKE 363.15   1.35    359.80      361.40    6          12          420.00 What's peculiar is that the price is significantly higher than the ask price. The question ...
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1answer
69 views

Option Pricing - Incorrect price outcome for Out of the Money (OTM) calls

I have the options data for a stock - ...
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49 views

Selling American calls before ex date vs. exercising

From reading Hull OFOD (among other references), I understand that early exercise makes sense for an American call option at time $t_n$ when $$D_n > K\Big[1-e^{-r\big(T-t_n\big)}\Big]$$ for a call ...
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116 views

Deriving Bachelier Greeks

I am working on the Bachelier Model with r not equal to 0 as described in the first and most upvoted answer in following link: Bachelier model call option pricing formula This is fairly easy to code ...
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1answer
71 views

is implied volatility derived from the option bid quote or the option ask quote?

I got SPX option prices from three different market data sources. In all of them, I can see bid and ask quotes. However, there is only one implied volatility. Does this implied volatility correspond ...
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97 views

What is the intuition behind a positive theta for European long puts?

I've googled extensively for an answer to this question. Very similar (if not identical) questions have popped up in this same website (example) but I never find the answers to be clear and/or precise....
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30 views

N-period state price deflators

Given that the non-dividend paying share is at $5. In each 6 future 6 month period its value can either rise by 25% or fall by 10%. The continuously compounded risk free rate is 5% p.a. Consider a ...
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103 views

Confusion Regarding Dynamically Delta Hedging a Short Option

To my understanding, market makers (mm) in the options market dynamically delta-hedge their portfolios by buying/shorting the underlying, thus eliminating directional risk and profiting from providing ...
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110 views

Data source for FX options

I have daily quotes for the new york and london fixings of fx options on EURUSD. I can choose between two sources: BGN and CMPN. Apparently these are based on slightly different methods of aggregating ...
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113 views

FX option quotation in interbank market

I am looking at the different ways in which FX options (say EUR/USD option) are quoted in interbank markets. Is it quoted using the option chain? I also saw a piece where it is said that it is quoted ...
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54 views

Is there an analogous strikeFromDelta implementation for 1st gen barrier options?

I have a simple replication pricing implementation for 1st gen exotics (digitals, single and double barriers, etc.). In order to effectively test strategies I want to price "like" strikes ...
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149 views

What is the probability of touching point A first?

The probability of a stock touching a point A which is below the current spot price is 35%, and the probability of the stock touching a point B which is above the current spot price is 20%. How can I ...
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CMS cap has more vega exposure than CMS floor for same strike

When I priced a 10y expiry single look CMS30 ATMF CAP, I noticed that the vega exposure is higher than that of the same 10y expiry single look CMS30 ATMF FLOOR. Why is that? I have a suspicion that it ...
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Unitise an options portfolio

Suppose I have a portfolio of European index options (long call, short put) and risk free assets (buy bank bills) to create a synthetic long index position. I wish to unitise this portfolio to ...
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125 views

What is delta of an option signaling?

In an interview I was once asked what the delta of an option was and my answer started from the fact that it is the first derivative of the option with respect to the price, and then I concluded ...
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97 views

Alternatives to RDBMS for options backtesting

I've assembled a large dataset (~2B+ records) of options price data in MySQL for backtesting purposes. At a number of points, due to the sheer amount of data being retrieved and filtered, processing ...
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133 views

How is Emanuel Derman's implied tree model implied volatility skew derived?

I am reading Emanuel Derman's paper Patterns of Volatility Change. The section, Implied Volatility In The Sticky Implied Tree Model has the linear skew approximation near the old underlying $S_0$ $$\...
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72 views

Using delta as probability of an option expiring in the money

I understand that delta can be seen as a probability proxy for an option expiring in the money, as well as deltas for call options ranging from 0 to 1 and deltas for put options ranging from 0 to -1. ...
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51 views

what is option zeta?

Is this an option greek? I've come across this term in some option book, and also online definition e.g. HERE: A measure that captures the premium difference between the value of an option calculated ...
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66 views

Reference for path dependent options

I want to study path dependent options for which I am following the book Paul Wilmott on Quantitative finance.But here I dont find the detailed explanations or derivations for the various PDEs .So is ...
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61 views

Difference in pricing of American call and put

In Paul Wilmotts quantitative finance books he says that the the value of an American option satisfies the following $$ \frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2 \frac{\partial^2V}{\partial ...
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43 views

How to price a risk reversal for common dice gain with chance to re-roll

I was just thinking about an extension to the common dice throwing interview expected value question: Question: Imagine a game where you throw a die and get a payoff equal to the number shown by the ...
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71 views

Independent variable in pricing of strongly path dependent options

I am reading Paul Wilmott on quantatative finance where he discuss the pricing of strongly path dependent options.The payoff at expiry T depends on the path taken by the asset in the sense that it ...
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119 views

How to derive the relationship between gamma and theta?

I am trying to derive this formula Θ = –0.5 × Γ × S^2 × σ^2 to see where it comes from. My thinking is that PnL = delta dS + Vdσ + 0.5Γ(dS)^2 + Θdt. Assume we delta hedged and vega hedged, first and ...
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MOC or TAS mechanism to trade stock options?

Wonder if anyone can help. Is there a product or mechanism to trade cleared stock options at the settlement price, in the same manner to Market on Close orders or Trade at Settle on commodity markets?...
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49 views

Computing the denominator of diluted earnings per share

I'm practicing for CFA level 1, and I faced this question. I don't understand the last part (802 − 481 = 321) because I understand that a company doesn't realize options of its own shares, if you are ...
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94 views

What does it mean to be long the skew?

Consider an equity option such as SPY and I'm long the skew, do I make money if puts raise in price and calls decrease or the opposite?
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105 views

How is delta defined as a unit?

This is going to be a embarrassingly basic question. But the answer seems to be hard to find. What does, say, selling, $d$ delta of calls mean? How is the "delta" defined? I am not asking ...
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57 views

Best way to measure time to expiration for options?

From my reading it seems that only trading days should be accounted for when calculating time to expiration. On the other hand, I see that VIX is calculated using every day until expiration without ...
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69 views

Early exercise American Options with Dividend

this is a basic question but I have not fully understood it. Let's say we have dividend paying stock (continuous dividend yield), when would we exercise the Option early? Since the Dividend yield is ...
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112 views

Question about pricing forward start option with Heston Monte Carlo

I'm trying to price a forward start option with payoff $\Big(\dfrac{S_{T_2}}{S_{T_1}}-1\Big)^+$ with Heston Monte Carlo. Heston Model: $$ dS_t = rS_tdt + \sqrt{v_t}S_tdW_t^1$$ $$ dv_t = \kappa(m-v_t) +...

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