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3
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1answer
61 views

Qualitative properties of call

I have read somewhere that we can show by using arbitrage argument the following relationship for call option : $$\frac{\partial{C_t(T,K)}}{\partial{K}}\leq0$$ ...
1
vote
1answer
42 views

Put call parity: when are the premiums the same?

Please explain why put call parity could be compared to the payoff of a long forward contract. ie. $C_E-P_E=V_X(0)$ where $C_E,P_E$ are the call/put premiums and $V_X(0)$ is the value of a long ...
0
votes
0answers
31 views

Connecting Call price computed discretely to call price computed under continuous time case

I want to connect the call premiums calculated discretely via the binomial pricing method to the Black-Scholes-Merton formula for the call premium which applies to continuous time case. The framework ...
0
votes
3answers
50 views

buy asset after exercising call options

Suppose that I buy a call option at \$10 for a stock $S_0 = \$100$, $K = \$110$, expiry date $T$. In $T$, $S_T = \$140$, so that I exercise the option to buy and then sell the assets (buy at $\$110$ ...
4
votes
0answers
55 views

Greeks of a Basket Option

I want to estimate delta, vega and gamma for a basket option. This option is a European Call option. The underlying is $S=\omega_1 S_1 +\omega_2 S_2$ Where: $S1$ = stock price of asset 1 $S2$ = ...
0
votes
1answer
56 views

Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff; Could you ^please help me !
0
votes
0answers
47 views

Delta of an option in two cases

Let C be the prime of a call in fi=unction of the price in term F, Strike K, volatilité $\sigma$ and maturity t: $C(F,K,\sigma,t,r) $ We assume that we know $\delta$ ...
2
votes
3answers
117 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
2answers
94 views

Analysis of exercising a call option early

Most options traders sell their call options early instead of exercising them, as you would make a bigger profit this way due to being able to salvage some remaining extrinsic value. For example: ...
4
votes
2answers
593 views

How many monte carlo runs do I need for pricing a Call?

I have to price several calls using Monte Carlo. Obviously, there is a huge tradeoff between the number of runs and the fair price of the call option. I know I can check how the approximation changes ...
0
votes
0answers
22 views

Price of call (calibration)

I need to understand how we got this : $\forall i \in I $ $C^{*}_{0}(T_i,K_i)=e^{-rT_i}E[(S_{T_{i}}-K_i)^+|S_0]=e^{-rT_i+X_{T_{i}}}E[(S_{T_{i}}-K_i)^+]$ at How we pass from conditional expecation to ...
2
votes
1answer
36 views

Understanding the necessary and sufficient conditions for rational early exercise of a call option

I am self-studying for an actuarial exam, and I encountered the following in my text: The author states that if $PV_{t, T}\text{(Divs)} < K(1 - e^{-r(T - t)})$, early exercise is not rational. ...
1
vote
2answers
82 views

difference between caplet and call

I wanted to know the difference between a caplet and a call. In my course (Interest rate models and curves) , we said that a caplet is a call option. Is it really true? Thanks
1
vote
0answers
27 views

Volatility Skew for Put and Call options [closed]

Given that the implied volatility follows volatility skew, which one has higher implied volatility? At-the-money put 40 (spot = strike = 40) or at-the-money call 160 (spot = strike = 160)? I am not ...
2
votes
4answers
105 views

pricing american calls on non dividend paying stocks

It is never optimal to exercise an american call option early if it is written on a stock that doesn't pay dividends, yet when pricing such an option, using a binomial model, we check whether or not ...
4
votes
3answers
91 views

Abritrage when Put Option Greater then Strike Price?

I am having a tough time conceptualizing this question here: Let $P$= Price of European Option, $S$ = Present Price of Option and $K$ = Strike Price. If $P > K$, why does abritrage exist? Assuming ...
1
vote
2answers
139 views

How do you calculate price of non-existant call option on commodity future

I've been stumped on this for awhile now. I'm trying to determine the price of a call option on a commodity futures contract that expires in the future. My issue is that while the future's contracts ...
1
vote
1answer
20 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 ...
2
votes
4answers
213 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 ...
1
vote
2answers
365 views

Estimate simple option price without a calculator

I have been to two different interviews for jobs related to option trading, and both time I have been asked a question, which is pretty basic, and still I could not answer it. If you have an European ...
2
votes
1answer
91 views

Quick way to extrapolate call price as function of strike

Let's say I know the price of a call for two different values of strike. Is there a quick way to guess the price for another value of strike ? Actually, I know that C(100)=15 and C(90)=20 and I have ...
0
votes
1answer
53 views

Pricing of a call option in one period binomial model

You are given a $5\%$ call option worth $\$2.66$. The strike price $k$ is $\$41.00$. $S(0)=40$, $Sd=35$ (i.e the lower price of the stock at $t=1$) find $Su$ (i.e the high price of the stock at ...
1
vote
1answer
33 views

What is the strike of a short put that mimics a covered call

If I am long a stock $X$ which I purchased at $\$100$ and sold a covered call in the front month with strike $\$105$ for $\$2$ then is it true that the covered call is equivalent to a naked put at ...
3
votes
2answers
106 views

arbitrage opportunity in a two period model

I have a little problem evaluating an european call. I Suppose the following: in $$t=0 : S_0 = 10$$ $$t = 1 : S_1 = \{10,11\}~with ~p=0.5$$ riskless rate : $(1+r)=\beta=1.049$ Strike ...
6
votes
3answers
2k views

What does it mean to be “long or short in volatility”?

I've heard a question regarding pricing of european calls. The question is: Is the call long or short in volatility when it is (deep) OTM? What is the profile of the implied volatility? I ...
1
vote
2answers
168 views

How to price an European call on zero-coupon from the yield curve?

It is known that the price of an European call of maturity $T^*$ on zero-coupon of maturity $T$ is given by $$p(0,T)= B(0,T^*)\mathbb E ^{\mathbb Q_{T^*}}\left[ (B(T^*,T)-K)^+\right]$$ where ...
2
votes
1answer
134 views

Will pricing a Bermudan option default to a value of a European option?

I have a call option with 2 expiry in two years. For the first 9 months I cannot excercise the option. After that the I can exercise at any time. I am pricing this option using a binomial tree using ...
4
votes
1answer
134 views

At-the-money Call Spread approximation

In a trading manual I got during a course, the value of the ATM Call-Spread is approximated by $CS_{ATM}=\frac{1}{2}StrD+(F-m)\times\Delta CS$ The lecturer skipped the part where he derived this ...
1
vote
2answers
544 views

fair price for a call option

I am struggling with the following problem: An investor is considering a European call option, whose price $C_0$ is yet to be determined, on the shares of a company called XYZ. You know that : the ...
0
votes
2answers
289 views

How is holding an European call option equivalent to holding an asset-or-nothing call option and writing a cash-or-nothing call option?

The cash-or-nothing call option has a payoff that is equal to the strike price. All three options have the same expiry date.
2
votes
2answers
384 views

Calculating Greeks in Covered Calls?

Just want to confirm whether Delta, Gamma, Theta, Vega will be calculated in the following way? Since we own 100 shares of stock while selling a call we need to subtract greek value from one? right? ...
5
votes
1answer
401 views

Why is the Put-Call Symmetry model dependent?

The put-call symmetry states that C(S,t;X,r,q) = P(X,t;S,q,r), and that this works for American options. According to my notes, this is 'model dependent' because it ...