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.

learn more… | top users | synonyms (1)

0
votes
1answer
15 views

What is the correlation of stock options?

I want to calculate the VaR of two correlated option positions, and I know the correlation between stock price returns. I want to separately calculate $Var_1$,$Var_2$ for option 1 and 2, and then use ...
0
votes
1answer
16 views

Gamma Imbalance Explanation

Can someone please give me an explanation as to what put-call gamma imbalance specifically refers to (imbalance of what?), and why they may exacerbate volatility from a market perspective, and why the ...
0
votes
1answer
41 views

Interpretation of vega out of BS formula

I am comparing Monte Carlo estimates of VaR (using importance sampling) under both the normal and student distributions. I am also considering risk factors other than log-prices; in particular, ...
0
votes
1answer
73 views

Feynman Kac Formula for path-dependent options

Consier geometric Brownian motion: $dS_t/S_t=\mu dt+\sigma dW_t$ Feynman Kac theorem tells us that the conditional expectation $v(t,x)=E[ e^{-rT}\Psi(S_T) | S_t=x]$ can be computed by solving the ...
0
votes
1answer
54 views

What exotic options are exchange-traded?

There are a number of exchanges that trade vanilla Call/Put American/European options on various underlyings (equities, indices, futures). There have been some trading in digital options on certain ...
0
votes
1answer
86 views

VIX Calculation - weighting of strikes

The formula for calculating the VIX from SPX options is given on page 4 of this document: https://www.cboe.com/micro/vix/vixwhite.pdf My question is, why is the option price at each strike weighted ...
0
votes
0answers
35 views

Risks Associated with Option Arbitrage Portfolio

If my math is correct, if I construct the following portfolio of options the worst that I can do regardless of what the underlying does is profit $1.74 (less commissions). Is this correct? Are there ...
0
votes
1answer
59 views

Citable source: Why implied volatility over dollar prices

I am aware of the reasoning of quoting vanilla options as implied volatilities rather than dollar values. However, I would like to have a literature reference where this is explained, to quote / cite ...
1
vote
1answer
12 views

Where do Over-allotment (Greenshoe) option shares come from?

I'm just wondering, if following an IPO the share price goes up and the underwriter calls the option, where do those extra 15% shares come from? Does the company have to issue more stock to cover the ...
1
vote
1answer
40 views

Option writing optimal sell time

When selling options, e.g. a straddle I read often the optimal time for selling options is 30-40 days until expiration. For me intuitively the optimal time would be around one week until expiration ...
0
votes
3answers
92 views

Is it realistic to assume that the current price of a stock takes into account the probability of it going up or down in the future?

I'm currently reading the following lecture notes: http://www1.maths.leeds.ac.uk/~jitse/math2515/lecture04.pdf On the second page, under the subsection titled "The Risk-Neutral World" it points out ...
0
votes
1answer
41 views

Can a large OpenInt of calls cause a stock to go down?

I read forum post from another site. Which stated... ...
1
vote
2answers
115 views

Linear combination of geometric Brownian motion

Let $X_t= e^{\left(\mu-\sigma^2/2 \right)t+\sigma W_t}$ be a geometric Brownian motion with drift $\mu$ and volatility $\sigma$. I am trying to find an analytical solution to $$\mathbb{E}\left[ ...
3
votes
1answer
125 views

Option prices in Bates SVJ model?

In this [post] discussed the European put and call price formulas under the Heston Stochastic Volatility model. There exists an important extension of Heston model to include diffusion jumps, known ...
0
votes
1answer
36 views

Difference between Closing Price, Last traded price and Settlement Price for option contracts?

What is the difference between Closing price, Last traded price and settlement price ? I got the difference between Closing Price and Settlement price from previous post : The difference between ...
1
vote
2answers
83 views

European call down and out option (geometric Brownian motion, Monte Carlo, Euler)

I need to estimate the expected value and the Greeks of an European call down and out option, assuming geometrical Brownian motion of the asset, with Monte Carlo simulation employing Euler ...
0
votes
1answer
95 views

Numerical Solutions for PIDE

I want to solve an exotic options of PIDE by Numerical Methods.I just focus on the integral part of PIDE and want to underestand some tips on numerical solution of how to numerically solve it. Exactly ...
3
votes
2answers
111 views

American vs European Options on equity index options

I have a question regarding the usage of European vs American Options. According to Professional Risk Mgr Handbook 2010, American-style options are used mostly on equities whereas European-style ...
1
vote
1answer
46 views

Negative adjusted strike in Levy's Asian option approximation?

In Edmond Levy's 1992 paper, he introduced a moment-matching method to approximate the price of an Asian option assuming GBM for the underlying. It suggested that, if some monitor points are already ...
0
votes
4answers
80 views

analytic formula for the value of an American put option

It seems to be a foolish question but I can't take my mind off from , Is it true that there is no analytic formula for the value of an American put option on a non-dividend-paying stock (or a divident ...
0
votes
0answers
35 views

What's the risk-neutral expectation of the arithmetic average of stock price?

All Black-Scholes assumptions apply ($y$ is yield): what's $E(A_T), E(A_T^2)$ and $Var(A_T)$ where $A_T=\frac{\int_0^T S_tdt}{T}$ is the continuous-sampling arithmetic average of the stock price ...
2
votes
0answers
74 views

Simulation of Heston process

I am currently working on implementing Heston model in matlab for option pricing (in this case I am trying to price a European call) and I wanted to compare the results I obtain from using the exact ...
0
votes
0answers
14 views

negative yield (interest rate) and Option Pricing [duplicate]

If i have negative yield (interest rate) can I still proceed with Standard Black and Scholes or Simple Binomial Model? any Adjustment is required to the model? how does it effect the pricing model in ...
1
vote
1answer
42 views

Calculate put price with Black-Scholes and one discrete dividend

I try to solve this exercise: a) Calclculate the price of a 3-month European put option on a non-dividend-paying stock with a strike price of 45 when the current stock price is 40, the risk-free ...
0
votes
1answer
58 views

American put option and rising interest rate

Will a rise in interest rate always result in a lower price of an American put option?
5
votes
2answers
144 views

how we can derive $PIDE$ of double exponential Jump-diffusion model (we know as kou model)?

I'm working in double exponential Jump-diffusion model (we know as kou model) with following form , under the physical probability measure $P$: \begin{equation} ‎\frac{dS(t)}{S(t-)}=\mu‎‏ ‎dt+\sigma ...
2
votes
1answer
46 views

Forced to exercise gap options

I was reading a textbook and came across some surprising stuff in the section about gap options. Let $X$ be a payoff function such that $X=\Big\{\matrix{0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...
3
votes
2answers
51 views

Implied volatility and nonconstant volatility

John Hull states in his text that "AS the maturity of the option is increases the percentage impact of nonconstant volatility on (option) prices becomes more pronounced, but its percentage impact on ...
2
votes
1answer
76 views

VaR calculation methods of options

I am a little bit confused about VaR in Options and I need a clarification for. I collected the following formulas, can you suggest what is the best formula and explain me why, please?
1
vote
0answers
21 views

In this scenario could gamma be higher for OTM options?

Let's say there is a $1 stock, with say 1 day to expiration. The 1.5 strike call, is probably a 0 delta at this point; however, a 1 point increase would mean the stock would be at trading at 2 ...
3
votes
1answer
208 views

Closed form solution of PDE of Option Price

Let $V=V(S_t,t)$ be the option price and \begin{align} V_t+\mu\,S\,V_S+\frac{1}{2}\sigma^2\,S^2\,V_{SS}=0\\ V(S_T,T)=\ln (S_T)^{2}. \end{align} My question: How can I obtain a closed form solution of ...
3
votes
2answers
107 views

Do futures follow physical or risk-neutral distributions

I've spent a while looking for an answer to this question and while I feel it is a simple question I have not found an answer. I know prices of option contracts follow an implied, risk-neutral ...
3
votes
1answer
36 views

Boundary Condition for Convertible Bond under Two-factor Model Interest Rate

I want to find Boundary conditions for Convertible Bond under Two-factor Model Interest Rate.The portfolio contains stock where stochastic differential equation for the stock price is \begin{align} ...
4
votes
2answers
204 views

good R package for vectorized option pricing

I am using for now the package fOptions but it doesn't allow for vectorized computation of black76 prices and delta. Which package can be used to do that? As noted ...
3
votes
1answer
42 views

Why risk-free interest is needed for Margrabe's Formula?

The source code for Margarble's formula in QuantLib is here. The implementation requires a forward price be computed: ...
3
votes
1answer
79 views

Numerical example of how to calculate local vol surface from IV surface

I'm looking for an excel example (not a copy of Dupire's eqn) of how to convert an IV surface to a local vol surface. If unsuccessful I'll work through Dupire's eqn but would be helpful to look at an ...
2
votes
3answers
140 views

Why can't you arb skew by buying options with low implied vol and selling high implied vol in the same month and dynamically hedging?

there's something I've been trying to understand for a while now and I just can't quite understand with regards to skew. In the same month, why can't you buy a option that have low implied vol on the ...
2
votes
1answer
97 views

Boundary conditions of PDE from SV model with stochastic interest rate

The PDE for the American put option price $P(S,\sigma ,r,t)$ is \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + ...
0
votes
1answer
66 views

Local volatility parametrization using the spot

Is it possible to estimate the local volatility using the spot price S at time t instead of the strike price K and the expiry date T ? Any help would be appreciated.
1
vote
2answers
81 views

Hedging portfolio and extraction PDE of SV model with stochastic interest rate

How can I extraction this PDE \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma ...
2
votes
1answer
81 views

Options on Volatility Control Index

I have two question. Does an option on volatility control index exist? If I google it, it seems like there is such an option, but I can't find the option on any of exchanges. So this is my first ...
0
votes
0answers
24 views

Intermediate Project Presentation

I would like to know an ideal plan for explaining/representing Greeks (1st,2nd,3rd) order. The topic seems to be quite vast and very interesting but not possible to cover within a 15 mins time frame, ...
1
vote
0answers
63 views

Price of an American call option [closed]

I'm working through revision questions at the moment and we are asked to compute the price of an American call option. Suppose that $dS_t = \sigma S_t dW^*_t, S_0 >0$ Let $0<U<T$ be fixed ...
2
votes
1answer
105 views

How to hedge a put under the Black-Scholes model?

To hedge a call, one would invest the option price proceeds into $\Delta_t*S_t + B_t = c_t$. (ok) However, a put has negative delta, so I would short $\Delta_t*S_t$ and invest ...
0
votes
0answers
42 views

Benchmarking option pricing under stochastic interest rates

I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates. Is there a way (e.g. a benchmark) to ...
2
votes
0answers
33 views

replicating strategy three step binomial

I am having some trouble setting up a replicating strategy for a call option with a three step binomial model (discrete). I have no trouble doing this in a two step binomial model by backward ...
0
votes
1answer
79 views

“Hedging” a put option, question on exercise

I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I: Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike ...
3
votes
1answer
108 views

Distribution of Black Scholes call option price at time 0<t <T

Does anyone know how to find the probability law (distribution) under P* of a Black Scholes Call Option price $C_t$ for $0 < t < T $? (Under P*, $ dC_t = \frac{\partial c}{\partial s}\sigma S_t ...
1
vote
2answers
193 views

Option arbitrage with dividends?

If a stock pays a discrete dividend, the stock price falls by the amount of the dividend. There is no arbitrage opportunity from this predictable jump, because the investors receive the same amount of ...
2
votes
4answers
204 views

How to short an option?

It appears to me that retail investors can only buy calls and puts, but not short them through any standardized way (except maybe borrowing the option from a friend ;) ). Is that correct, or how can ...