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)

1
vote
1answer
48 views

How should I understand expiration dates?

The following is an excerpt from Introduction to the Mathematics of Finance by Roman: Expiration Dates The last trading day of an option is the third Friday of the expiration month and the ...
1
vote
1answer
49 views

Implied Expected Stock Return from European Option Prices

We can calculate the expected stock return (under the measure $Q$) from at-the-money ($K=S_t$) option prices as: $$E\left(\frac{S_T-S_t}{S_t}\right)=\frac{e^{rT}}{S_t}(C_t-P_t)$$ The result is ...
1
vote
2answers
435 views

CME historical option data provider

Is there any other historical end-of-day CME option data provider rather then CME DataMine? I've searched all the internet and found only CBOE traded options.
3
votes
2answers
76 views

How is the Chooser Option's value computed in this example?

In preparation for my finals, I am attempting a question on chooser options. One question asks A European chooser option on an index ETF paying a yield of 3.0% with strike \$64 has a maturity of ...
2
votes
2answers
120 views

Carr-Madan Formula

Really new to financial Maths. I am currently having problems with the Carr-Madan Formula. $$f(S_T)=f(F_t) + f'(F_t) (S_T - F_t) + \int_0^{F_t} f''(K) (K-S_T)^+ \ d K + \int_{F_t}^{\infty} f''(K)...
1
vote
1answer
82 views

How to understand this example from Hull's book?

I just started reading Hull's book, and I got stuck in an example where a financial institution has sold for $300,000 a European call option on 100,000 shares of a non-dividend-paying stock. Stock ...
2
votes
2answers
56 views

Why would one prefer variance swaps over other instruments?

I understand that an investor who has a view on an underlying's variance would be tempted by a variance swap. But why would one prefer such a contract over another instrument whose value is based on ...
5
votes
2answers
119 views

Solution for american perpetual put

I have been attempting an exercise in which I have to determine the value of an american perpetual put, $P$ in terms of the asset value $S$. The solution to the exercise says: When $S>S_f$ (the ...
0
votes
2answers
208 views

Where can I find best end of day option data? [duplicate]

Looking for accurate end of day option data. Preferably with Greeks. Any recommendations?
9
votes
2answers
312 views

Derivation of Stochastic Vol PDE

A couple questions regarding stochastic vol PDE derivation. Following Gatheral, a general stochastic vol model is given by \begin{align*} dS(t) & = \mu(t) S(t) dt + \sqrt{v(t)}S(t) dW_1, \\ dv(t) ...
3
votes
1answer
53 views

Deep ITM Call Implied Vol via Monte Carlo

Let's say I've computed the price of a call using Monte Carlo with $S_0 = 100$ and $K = 80$, using $T = 0.1$ and $r = 0$ to be $\$20.00095$. This price estimate comes with a $95\%$ confidence ...
2
votes
2answers
95 views

Option pricing, origin of formula $\Pi( t,X)= E^{\mathbb{Q}}\left[e^{-\int_{t}^{T}r_s\,ds} X| \mathcal{F}_t\right]$

Imagine a model with stock prices and dividends of these stocks, as well as a market bond with associated short rate process. It is known that this model is arbitrage-free if there exists an ...
1
vote
1answer
62 views

construct volatility smile based on historic observations

So I calculated historic volatility/skewness/kurtosis for a commodity. I now would like to construct a volatility smile that reflects this historically realized distribution. I tried using some ...
1
vote
1answer
35 views

Find the parameter $d$ of the Affine Option Pricing Model in Duffie, Pan and Singleton (2000)

According to Duffie, Pan and Singleton (2000) for any real number $y$ and any $a$ and $b \in \mathbb{R}^n$, the price of a security that pays $\exp(aX_t)$ at time $T$ in the event that $bX_t \leq y$ ...
1
vote
0answers
47 views

How can we observe volatility smile from the market. Drawbacks of Heston Stochastic Volatility Model

Here are two questions related to implied volatilities. a) The set up here is for an European option. We can get its implied volatility smile from calibration, the question is why could we also ...
4
votes
2answers
1k views

Options pricing exercise - American call option on a futures contract

I am confused by a particular exercise I am doing right now, I am hopeful that someone can walk me through as to how to solve it. I further hope the question is not considered too basic for this forum....
1
vote
2answers
224 views

Who Uses American Options?

...in other words, why would a person want to have the right to exercise an option early? What advantage does that really give you? Are Euro-style options not good enough for some people? Who are ...
0
votes
1answer
75 views

What models / methods are used in practice in derivative pricing?

I wrote my bachelor thesis about European Option Pricing under Stochastic Volatility and Jump Diffusion and am now near the end of my MSc in Quant Finance. As i want to write a "potential job"-...
0
votes
1answer
58 views

Delta Hedge, does large stock move produce a loss?

I dont understand how MM protect themselves from large moves in underlying while being delta hedged. Example: MM sels 1 ATM put and sells 100stock (delta = 1) as a hedge. Now what will happen if next ...
0
votes
2answers
42 views

In an example of “call options”

The following is an excerpt from Introduction to the Mathematics of Finance by Roman: As a more concrete example, suppose that IBM is selling for $\$100$ per share at this moment. A $3$ month ...
3
votes
1answer
85 views

Is This A Viable Alternative Options Pricing Method?

i'm currently a high school student who hasn't gone past Algebra II, and thus I have minimal Calculus knowledge. I know the basics of Integration and Derivation (drop the coefficient, raise to the ...
1
vote
0answers
35 views

Is it possible to place hidden order inside spread when trading E-mini S&P 500?

My question is not about hidden orders in general. In equity market a trader can post his hidden order inside spread, is it the same way for E-mini S&P 500?
6
votes
2answers
407 views

How to derive the price of a square-or-nothing call option?

At maturity $T$, the holder of a "square-or-nothing" call option written on an underlying $S_t$ receives a payoff of the form $$ \phi(S_T) = \frac{S_T^2}{K} \pmb{1}_{\{S_T \geq K\}} = \begin{cases}\...
0
votes
0answers
34 views

Estimate Option Price Given X% Move N Days in the Future

I was wondering if someone could recommend a method to estimate the price of an option N days from now given an X% move in the underlying. I have fitted a volatility surface but where I am running ...
2
votes
1answer
57 views

Why is H always* the letter used to describe the level of a barrier?

A quick and (hopefully) easy question. Why? *(always / often / when it's not B)
0
votes
1answer
40 views

Does a Call Spread always need to be symmetric?

I have a plot of a Call Spread Option at time $t ={0}$ but the graph of the call spread is not completely symmetric. My question is: does it have to be? Here is the plot I'm referring to: I'm just ...
3
votes
1answer
118 views

Boundary Conditions for Call Spread

I was just wondering if someone could verify whether these are the two boundary conditions for a Call Spread Black-Scholes PDE. The first one I have is: $max(S_{T} - K_{1}, 0) - max(S_{T}-K_{2},0)$ ...
3
votes
1answer
82 views

Carr-Madan european contingent claim payoff decomposition formula - application

Looking for some clarification to the values of the parameters used in the Carr-Madan payoff decomposition formula. $$f(S_T)=f(\kappa) + f'(\kappa) (S_T - \kappa) + \int_0^{\kappa} f''(K) (K-S_T)^+ ...
1
vote
0answers
19 views

Pricing with-profit/smoothed bonus annuity using Black-Scholes

Would this be possible? Subsequently, would the pricing of such an annuity be somewhat similar to pricing a lookback option?
1
vote
1answer
28 views

Is it possible to find / estimate the volatility surface of non-listed index options?

I have 3 QNET options (european, 2 puts, 1 call, all same expiry, different strikes) that the broker is pricing clearly off a volatility surface. Bloomberg only carries historical volatility and I ...
4
votes
3answers
6k views

Does implied vol vary for calls vs puts?

Volatility skew tells us that options with the same maturity at different strikes can have different implied vol. However, can a corresponding call and put for the same strike and maturity have ...
0
votes
1answer
58 views

Accurately calculating Greeks for options near expiration

I understand that when a vanilla European option is near expiry, the Theta calculated from BS formula is very inaccurate and almost meaningless for practical use. However, I'm not sure if other ...
1
vote
0answers
106 views

Numerical Methods for Merton Model

The stochastic differential equation for an underlying with jumps in Merton model is: $$d{{S}_{t}}=\mu \,{{S}_{t}}dt+\sigma \,{{S}_{t}}\,d{{W}_{t}}^{P}+(J-1){{S}_{t}}d{{q}_{t}}$$ where $t \quad\,\,\, ...
3
votes
1answer
112 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 ...
1
vote
1answer
79 views

Differentiating a Payoff

Okay this is probably going to be an extremely easy/straightforward question but I thought I should post it here just to double check. Suppose I have a payoff $\Phi = (S_{T}-K)^{+}$. Now let's say I ...
6
votes
3answers
161 views

Creating Options Database

I am trying to create a database which will hold information for various stock options and will need to be updated daily. The idea is to use this database to keep track of changes in the open interest ...
0
votes
0answers
31 views

American call early exercise, considering a portfolio

Im aware there are lots of questions about this, but I am interested in a particular method of showing why an american call (with no dividends) should not exercised early. Here is the text I'm ...
0
votes
1answer
39 views

When is option value inversely related to expected volatility?

It is common knowledge that the greater the expected value, the higher the option value. However, there are surely exceptions, as written by Paul Wilmott's FAQs in Quantitative Finance Q: If you ...
7
votes
2answers
231 views

How to price an option allowing to change a call into a put?

A recruiter asked me this question: Suppose you have the following contract: a call option with maturity T = 2 years the possibility to change this call into a put at t = 1 year What is the price ...
7
votes
3answers
1k views

How to exploit calendar arbitrage?

Say we are looking at European Call options in a toy environment with zero deterministic intereset rates, a stock paying no dividends, no repo rates etc. Let C(T,K) be the price of a call with expiry ...
1
vote
1answer
65 views

Option delta - Conditional probability definition?

Can someone help me interpret this definition of delta? Delta is a conditional probability of terminal value (St) being greater than the Strike (X) given that St > X for a call option. Is the ...
2
votes
0answers
76 views

Problems with a Black-Scholes modified equation

I haven't really studied much financial mathematics until about 2 months ago so I'm quite new to this stuff, so I'm sorry if this is a trivial question. At the moment I'm trying to work out what the ...
11
votes
5answers
4k views

Best way to store hourly/daily options data for research purposes

There are quite a few discussions here about storage, but I can't find quite what I'm looking for. I'm in need to design a database to store (mostly) option data (strikes, premiums bid / ask, etc.). ...
3
votes
4answers
160 views

Black-Scholes formula proof, without stochastic integration

I've looked into many books at my academic library, and very often it goes like this: Brownian motion Then, stochastic integration (Itô's formula etc.) Application: Black-Scholes formula for price ...
1
vote
1answer
42 views

Old CBOE SPX options data: listing and expdate issue

I can't figure out the logic behind SPX option data for 2008-2009 years. First, all traditional SPX options have exp_date on the third Saturday of each month. How can it be? Why not Friday? Second, ...
0
votes
2answers
34 views

Combos on close SPX

I am wondering if anyone has any information on how combos on close trade. I've been looking at the BTIC (http://www.cmegroup.com/trading/equity-index/btic-block-trades.html) and was wondering if ...
4
votes
1answer
81 views

What are the answers to these questions on card deck and option pricing?

here are 3 questions I have some trouble dealing with. Your help will be greatly appreciated! 1 - We have a deck card: 26 red, 26 black. we play a game: you draw a card from the deck without putting ...
3
votes
1answer
69 views

Why can a swap option be regarded as a type of Bond option?

Why can a swap option be regarded as a type of bond option? My idea: Suppose the swap rate of the swaption is $s$. Now consider a bond option expiring at $T$ with strike, $(P_K)_t = \dfrac{1}{1+s(T-...
0
votes
1answer
44 views

Payoff of option

Consider the payoff $g(S_T)$ shown the figure: I believe the payoff represented as a linear combination of the payoffs of some options with different strike and same maturity $T$ is $$g(S_T) = (...
6
votes
2answers
223 views

The Upper Bound of an American Put Option

I have just read the following paragraph (in bold) and have a question on the upper bound of an american put option: http://www.sharemarketschool.com/option-valuation-upper-and-lower-bounds-part-...