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.

Filter by
Sorted by
Tagged with
3
votes
2answers
3k views

backtesting options strategies in R

I would like to backtest an options strategy in R. I require the ability to delta hedge and rebalance to options in the portfolio at different frequencies (daily, monthly,etc.) What packages are the ...
3
votes
3answers
423 views

Implied volatility of a complex options position

Assume I have a "complex" options position like a straddle, strangle, or iron condor. In other words, several options traded together as a single position against one underlying asset (not a basket ...
1
vote
3answers
395 views

How does Rho behaves with moneyness of option?

I was trying to find the relationship between nature of Rho and moneyness of the option. After finding certain values I found that Rho Value keep increases as the option gets further in the money. ...
0
votes
1answer
331 views

probablity expiring in the money ..basic question

Everyone says $N(d_2)$ is the probability of the option being exercised but stocks that have really high volatility have really expensive options indicating a high likelihood of expiring in the money. ...
8
votes
2answers
751 views

What changes to put-call parity are necessary when evaluating american options on non-dividend paying assets?

If an underlying doesn't pay dividends (for our purpose defined as any distribution to the underlying's holder) directly or indirectly (e.g. options on futures) how does put-call parity change from ...
7
votes
1answer
1k views

Need historical prices of EUREX American and European style options

I am trying to get the historical price data on selected American and European style options at EUREX. I am not familiar with their system. Does any one know whether they have something like yahoo ...
4
votes
1answer
115 views

Expected payoff at future time

Let $a$, $b$, $c$, and $e$ be constants, $W_1$ and $W_2$ be Brownian motions with correlation $\rho$, and $f(t)$ and $g(t)$ be deterministic functions of time. Let $X$ satisfy $$d(X(t))=(aX(t)+ef(t)g(...
3
votes
2answers
1k views

Vega and Gamma signs

Do vega and gamma always have the same sign (ie both positive or both negative)? Under what circumstances can they have opposite signs?
3
votes
1answer
171 views

How to derive an option price for an asset with these dynamics?

Assuming my underline asset price follows the process: $$d\ln (F_{t,T})=-(1/2)\sigma ^2e^{-2\lambda(T-t)}dt+\sigma e^{-\lambda(T-t)}dB_t $$ How should I derive an option price formula?
3
votes
1answer
197 views

Why are there two expressions for the Black-Scholes hedging portfolio

I am new to derivatives pricing and am trying to understand why there are two different expressions for the Black-Scholes hedging portfolio. The first approach, used in books like Hull, stipulates ...
3
votes
1answer
159 views

Dependency of an option price on time till expiry

I am trying to seek satisfaction when it comes to understanding why the price of an option is dependent on the time until expiry. I have read that the longer till expiration, the more time available ...
2
votes
1answer
203 views

SABR PDE spot/forward upper boundary condition implementation

When running my Finite Difference code, I observe something odd. Although implementing a classical (non-reverting) SABR model, I initialized the variables such that it should be equal to Black-...
2
votes
0answers
166 views

Discrete time option gamma hedging

1) An option $V$ under the Black-Scholes model is perfectly hedged when it is delta hedged continuously with the underlying $S$. When the hedging time is discrete, the delta $\Delta$ needs to take ...
2
votes
1answer
242 views

Cumulants of variance gamma with stochastic arrival (VGSA) model

The characteristic function of the VGSA model is defined as a specific parameterization of the characteristic function of the CIR (Cox-Ingersol-Ross mean reverting process) time-change: $ \mathbb{E}e^...
2
votes
2answers
454 views

Calculating time value of an option

Can someone provide me with a robust way of calculating the future time value of an option or point in the direction? I have been reading a lot about the factors that affect it and about betas and ...
2
votes
1answer
482 views

Calculating probability of options with normal/lognormal distribution: does time make a difference?

I'm trying to calculate the probability of a calendar spread resulting in a profit at expiration, when estimating it is modeled as a lognormal distribution, by getting: ...
2
votes
1answer
334 views

Question on OptionMetrics: when are adjustments for discrete dividends needed?

Bakshi et. al. (1997) analyzes the empirical performance of some alternative option pricing models. I am interested to do this as well - hence applying different models - but I am unsure how to handle ...
2
votes
0answers
127 views

Binomial Model Implementation Trouble - American and European options come out equal

I'm Trying to implement the binomial option price model in python and get reasonable performance by using memoization. I checked the output against a black and scholes model and for European options ...
1
vote
1answer
601 views

Option greeks as dollar P&L

If I write the value of an option as O(S, K, T, V), where S is the underlying price, K is the strike, T is the time to expiry and V the implied volatility, how can I compute the dollar amount that I ...
1
vote
1answer
177 views

Upper bound option price in volatility dimension

All, I have a theoretical question about the value of an option when spot price goes to infinity as a function of volatility going to infinity. I know that for a call option: The option value ...
1
vote
1answer
83 views

How to manage risk on a call calendar when underlying is falling

Let us say I bough a call calendar spread. Now, at expiry of the short option, the underlying has decreased significantly, and I am approaching my max loss(i.e both the options are close to 0). In ...
1
vote
1answer
55 views

Finding the extrinsic value of an option with conditions

Background: Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant. Let's also assume, that the correlation ...
1
vote
1answer
106 views

Cap option on Libor

We denote discount factor $D(t),$ zero coupon bond $B(t,T),$ $E_t[X] = E[X|\mathcal{F}(t)]$ and $T$-forward measure $E_t^{T}[\ ]....
1
vote
3answers
478 views

At-the-money and volatility smile

In a volatility smile; why is the ATM point usually or ideally at the bottom? In other words, why is the "smile" smile shaped as opposed to another shape?
1
vote
4answers
865 views

List of ISIN for Options, Swaps, Derivatives?

In pages like isin.org or openfigi you can search by an ISIN and you will get information about the share, bond, fund... However, for options , derivatives the search returns 0 results. Is there a ...
1
vote
2answers
4k views

Long/Short Vega and Option Positions

Why do you get long vega when you buy an option and short vega when you sell an option? I would have thought that for both buying and selling options the vega would change according to whether the ...
1
vote
0answers
72 views

AFV Model Implementation for Convertible Bonds

I am reading the original AFV model paper for pricing convertible bonds. https://cs.uwaterloo.ca/~paforsyt/convert.pdf The paper is very technical and I am having trouble finding the actual PDE's to ...
1
vote
1answer
222 views

Deriving Delta Hedge error in the B-S setup (part 2)

In this paper paper page 16-19 by Davis and this discussion derivation of the hedging error in a black scholes setup, the derivation of the delta hedging error in the Black Scholes model is discussed. ...
1
vote
1answer
163 views

What is the analogue used by Hull to price European calls with known cash dividends?

From The Book by Hull: And Hull's comment: This rule is analogous to the one developed in Section 14.12 for valuing a European option on a stock paying known cash dividends. (In that case we ...
1
vote
0answers
149 views

SPX/VIX Implied Beta Calculation

In https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true, it states that 3M VIX/SPX implied Beta = (VIX 3M IVOL*VIX 3M futures)/SPX 3M IVOL ...
0
votes
1answer
691 views

Interpretation of an option gamma larger than one

I am working on an option hedging simulation. In this context, I wanted to expand the simulation to include gamma. For testing purposes, I used among others the natural gas futures. When I calculate ...
0
votes
1answer
138 views

Possible to use diffusion equation(s) to price derivatives with non-zero boundary conditions?

One of the reason the Black-Scholes can be transformed into the heat equation is that calls and puts have a zero boundary condition on their contingent payoffs. Define the terminal payoff condition ...
0
votes
1answer
2k views

Price of call/put is convex in $K$ (strike price)

Let $\lambda\in(0,1)$. Then $$C(T, \lambda K_1 + (1 - \lambda)K_2, S, t) \leq \lambda C(T, K_1, S, t) + (1 - \lambda)C(T, K_2, S, t)$$ $T$ - the maturity $K_1$,$K_2$ - Strike prices $S$ - stock ...
0
votes
1answer
31 views

Is the assignment of exercised options “truly” random

Everyone seems to say that assignment of exercised options is random; does it just appear random to an outside viewer or does the exchange pick a name from hat for assignment?
-2
votes
1answer
422 views

How would you price an option with payout ln(St) where St is the stock price at time t

I know it has to be done through martingales, but I am not fully sure how to do this BSM pricing.