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.
2,078
questions
2
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64 views
+50
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 ...
0
votes
1answer
54 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 ...
0
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1answer
343 views
How to show arbitrage when a European option price is greater than the no-arbitrage price?
My example is:
Current price = 20,
If it goes up it'll be worth 22, if it goes down it will be worth 18
risk free rate: 12%, time = 3 months
Strike = 21
call option is worth 0.633
I know that if the ...
0
votes
1answer
95 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 ...
0
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0answers
63 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 ...
2
votes
1answer
79 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% ...
2
votes
1answer
202 views
What is the probability of a lookback option ending in the money (CRR-model)
I would like to compute the probability that a certain lookback option ends in the money, let's say that the option has the following payoff $h_N=\max\left\{0,K-\min\{S_1,...,S_N\}\right\} $ where $K$ ...
0
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0answers
48 views
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 ...
2
votes
2answers
867 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 ...
0
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0answers
69 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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vote
1answer
147 views
using bid ask prices to imply bid ask volatilities
Let's say i have bid / ask feed of an option prices (across strikes and expiries, calls and puts), what is the accurate way of implying out vols from these bid / asks
For eg; to get the bid vol, ...
0
votes
1answer
66 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 ...
1
vote
0answers
78 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 ...
3
votes
0answers
101 views
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, ...
1
vote
1answer
91 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 ...
1
vote
1answer
355 views
Options Weighted Vega Derivation
Does anyone have a good reference on how to derive time weighted vega for options? The only literature I found was in this presentation:
http://www.topquants.nl/wordpress/wp-content/uploads/2015/01/...
6
votes
2answers
11k views
How to Delta Hedge with Futures?
The theory of delta hedging a short position in an option is based on trades in the stock and cash, i.e. I get the option premium and take positions in the stock and cash.
In the classical no-...
3
votes
4answers
5k views
Value of Call Option as Volatility goes to Infinity
Why would the value of a call option go infinity as volatility goes to infinity?
I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
0
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0answers
37 views
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 ...
-1
votes
0answers
64 views
Is there any relationship between the straddle range and the trading range?
The short straddle has 2 breakeven points. It’s profit zone is between those breakeven points and I would call it the straddle range.
A straddle is sold which has X days to expiration. The underlying’...
0
votes
1answer
81 views
Evaluating swaptions with negative interest rates
Does anyone know if it is possible to evaluate swaptions with negative interest rates with Quantlib?
...
0
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1answer
136 views
Find the value of put option using a two-period binomial model
I've been asked to find the price of a two-month European Put Option with strike price $£40$.
The price at $S_0=£30$, this can move up to $£40$ or down to $£25$ ($1/3$ chance to go up, $2/3$ chance to ...
2
votes
1answer
100 views
Does time remaining matter in NO Touch-ONE Touch probabilities?
I asked a question some days back and got an answer which I understand and make sense:
Probability of touching short call strike and not touching touching short put strike of a short strangle?
However,...
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0answers
35 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 ...
1
vote
2answers
163 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 ...
0
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2answers
249 views
Storing options EOD time series in Flat Files
I have purchased data for EOD settlements of options prices for USA futures for personal use. I will not need multiple user access or real time access. I am not an expert programmer but use C# and R ...
0
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0answers
78 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 ...
0
votes
1answer
101 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 ...
4
votes
2answers
5k views
Why do ATM call options have a delta of slightly bigger than 0.5 and not 0.5 exactly?
From the formula of the delta of a call option, i.e. $N(d1)$, where $d_1 = \frac{\mathrm{ln}\frac{S(t)}{K} + (r + 0.5\sigma^2)(T-t)}{\sigma\sqrt{T-t}}$, the delta of an ATM spot call option is ...
0
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0answers
35 views
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-...
1
vote
2answers
167 views
Derivation for call option upper bound
In Euan Sinclair's book, Option Trading, he writes that $c <= S$, the price of a European call must be lower than the price of the underlying stock. To prove it, he applies the principle of no ...
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0answers
71 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 (...
11
votes
3answers
8k views
How to exploit calendar arbitrage?
Say we are looking at European Call options in a toy environment with zero deterministic interest rates, a stock paying no dividends, no repo rates etc...
Let $C(T,K)$ be the price of a call with ...
2
votes
1answer
147 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 ...
5
votes
2answers
287 views
Black-Scholes: Volatility Smile "sharpens" with time to expiry
I have tried to calculate IV and log-moneyness (=log(S/K)) for different times to expiry
(M = less than 1 month, Q = less than 1 quarter, S = less than 1/2 of an year, Y = less than 1 year, Y (+) = ...
0
votes
1answer
127 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 ...
4
votes
2answers
349 views
Gamma of interest rate derivatives
consider an interest rate derivative whose value $V$ depends on $n$ interest rates $r_1, \dots, r_n$.
Hence $V$ is a function in $n$ variables $V(r_1, \dots, r_n)$.
My question concerns the gamma $\...
-1
votes
2answers
125 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 ...
0
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0answers
41 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 ...
0
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0answers
41 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 ...
0
votes
0answers
30 views
Power options for pricing European claims
I have the following question:
Why would somebody be interested in the expression $E[S^\theta]$ for $\theta$ between zero and one.
The only thing I know is that this then can be somehow used to ...
1
vote
2answers
105 views
Approximating Volatility Skew From historic returns? [closed]
I was wondering if someone could help me with something. I've been reading more about equity options, and I'm struggling with skew. Conceptually I understand why it exists, what I'm struggling with is ...
4
votes
2answers
482 views
Is the Binomial Tree Model not self-financing?
Consider a 2-period binomial tree where the derivative price is $f$ and the stock price is $S$. Also, let the bond be deterministic with continuous growth rate $r$ and initial value $B_0$. binomial ...
0
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0answers
26 views
How to find probabilities of moves in a trinomial tree?
I'm given a non-dividend stock with price $p$ and volatility $v$ and given a European Call option corresponding to this stock.
I want to calculate the probabilities of the following moves:
$M_U = \...
0
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0answers
68 views
Generating Greeks with American Options
Investor and Software Engineer but very new to quant finance here...
I have the below code (which I'm sure will be helpful for some) and have some questions regarding the function parameters!
Is RF ...
2
votes
2answers
186 views
Autocall pricing: what does "Lipschitz continuous parameterization" mean?
I've been reading through this research paper (A Monte Carlo Pricing Algorithm For Autocallables That Allows for Stable Differentiation by T. Alm, B. Harrach, D. Harrach, M. Keller) about a method for ...
0
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1answer
126 views
No Probability in Greeks
In an interview, I was once told that I should not consider probability when talking about option greeks since from a mathematical point of view greeks have nothing to do with probability. That is of ...
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0answers
31 views
Possible to Pull Individual Option Purchases through YFinance/Script?
I am trying to pull live trade data through python using yfinance, however, I cannot seem to find any sort of command that can output physical purchases of options (ex. one person purchased 4 call ...
0
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0answers
57 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 ...
2
votes
2answers
126 views
Historical quotes / prices of multiasset options
I am working on Lévy copulas, and I would like to try calibrating such techniques on real data. Where can I find quotes for multi-asset options? It could be exchange options or any other type of ...