Questions tagged [call]

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8
votes
3answers
8k 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 know ...
8
votes
3answers
13k views

Bachelier model call option pricing formula

Does anybody have the Bachelier model call option pricing formula for $r > 0$? All the references I've read assume $r = 0$. I don't speak French, so I can't read Bachelier's original paper.
7
votes
1answer
677 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 ...
5
votes
1answer
306 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 ...
5
votes
0answers
678 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 $S2$ = ...
4
votes
2answers
1k 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 ...
4
votes
1answer
362 views

Equivalent form of Black-Scholes Equation (to transform to heat equation)

I am trying to understand the transformation of the Black-Scholes equation to the one-dimensional heat equation from Joshi, M. (2011). The Concepts and practice of mathematical finance. 2nd ed. ...
4
votes
5answers
835 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 of ...
4
votes
3answers
97 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 $...
4
votes
0answers
107 views

Zero-rebate barrier option pricing under the Heston model

I'm trying to derive an approximation for the zero-rebate barrier option under the Heston model: $$dS_t=\mu S_tdt+\sqrt{v_t}S_tdW^S_t$$ $$dv_t=\kappa(\bar{v}-v_t)dt+\eta\sqrt{v_t}dW^v_t,\quad d\langle ...
3
votes
1answer
100 views

Qualitative properties of call

I have read somewhere that we can show by using arbitrage argument the following relationship for call option : $$\frac{\partial{C_t(T,K)}}{\partial{K}}\leq0$$ $$\frac{\partial^2{C_t(T,K)}}{\...
3
votes
2answers
820 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? ...
3
votes
1answer
319 views

Delta Hedging/ Exchange for Currency Options

I'm looking at 2 cases of hedging EURUSD, using call spread or range forward. Lets say spot is 1.1300 and my buy call is at 1.1300 and sell call is at 1.1500. Hypothetically I'm assuming that this is ...
3
votes
1answer
131 views

Call option prices in terms of maturity with negative interest rates

let's assume that interest rates are constant, $r$. When $r\geq 0$, we can see that if $T_1<T_2$ and $C_1$ (resp. $C_2$) is the price of a call option on a non-dividend paying stock with maturity $...
3
votes
2answers
157 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 ...
2
votes
4answers
256 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 ...
2
votes
2answers
263 views

Flaw in the following argument with Binary Options and Skew

A Binary option is ATM and expires tomorrow. If the skew of the vanilla options steepens (left side up, right side down) what happens to the price of the Binary Option. I know that using a ...
2
votes
2answers
355 views

Black-Scholes call option formula, which probability measure

The stock and bond under the Black-Scholes framework, no dividends: $$S_t=S_0e^{\sigma W_t+\mu t}=S_0e^{\sigma \tilde{W}_t +(r-\frac{1}{2}\sigma^2)t}$$ $$B_t=e^{rt}$$ where $\tilde{W}_t$ is $\mathbb{Q}...
2
votes
1answer
98 views

How to derive and interpret the duration of a call option?

I read here that CFA students are taught that $$ D_{C} = \frac{\Delta_{C} D_{B} B}{C} $$ Where $D$ is the duration, $\Delta_{C}$ is the first derivative of the options price with regards to the ...
2
votes
4answers
565 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 ...
2
votes
1answer
230 views

How to price a call option which depends on two Wiener processes?

Could someone explain to me why the regular call pricing formula works, just with $\sigma$ replaced by $\|\sigma\|$ in the case where the underlying asset depends on two Wiener processes? For example,...
2
votes
2answers
2k 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 ...
2
votes
1answer
113 views

Explaining an Option product: SIX Discount Certificates

So I have the option with the important info above. I am trying to generate a portfolio that represents the option. However I am stuck on the first hurdle as I believe it is a call option as the ...
2
votes
2answers
631 views

Why it is not possible to price American perpetual call option using PDE approach?

Using a standard PDE approach to price an American perpetual put option I obtain that the price of such option has the following form: $$ V(S) = A S + B S^{-2r/\sigma^2}. $$ And then I need to find a ...
2
votes
1answer
96 views

How does gamma trading depend on $K$?

If we think realized vol > implied vol, then we might go ahead and delta hedge a call, hoping that profits from gamma outweigh the decay. Question: What should $K$ be on the call? ATM? If so, why? ...
2
votes
1answer
62 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. ...
2
votes
1answer
130 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 ...
2
votes
1answer
189 views

Fair value for a LEPO (Low Exercise Price Options)

In one of my lecture notes, I stumble across this exercise question: Consider Low Exercise Price Options, LEPOs, (with dividends) in Australia. Using the value at the outset, explain why such ...
2
votes
1answer
453 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 ...
2
votes
0answers
214 views

Callable Bond = long Bond - call on bond?

Can someone verify (maybe there is some literature around) the following relationships? Callable Bond= Long on Bond + short on a Call Position --> PV(CallableBond) = PV(Bond) - Call on Bond? or ...
1
vote
1answer
442 views

Call option with underlying following a Bachelier process

I am trying to reach a derivation/proof for how to price a call option when its underlying asset follows a Bachelier process with unknown drift term: $$dS_t=...dt+\sigma dW_t$$ but zero interest ...
1
vote
1answer
267 views

Call option Delta

I have an exercise where I need to show that the prices of call options $ C(t,K)=E((S_t-K)^+),t \in [0,T]$ with Strike $K$ for fixed $t$: $$\frac{\partial ^+C(t,K)}{\partial K}=-P(S_t>K).$$ We ...
1
vote
2answers
3k 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 ...
1
vote
1answer
39 views

Calculating the max. risk free interest rate with two given options

I have an excercise where we have two European Call Options, which have the same underlying, same maturity $t = 3$, same interest. The only difference is their price and their strike. The price of the ...
1
vote
1answer
134 views

Question about the process of monte carlo simulation

I have encountered an interesting question. Is it better to simulate the geometric brownian motion process for call itself or GBM for the underlying. My question is can we actually apply GBM to call? ...
1
vote
1answer
101 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 ...
1
vote
2answers
167 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: ...
1
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2answers
2k 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
1answer
108 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
47 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 ...
1
vote
1answer
84 views

Interest rates, effect on call price

Generally, we assume that an interest rate increase makes the call price more expensive. From my understanding it is because the expected return on the stock price increases. However the interest rate ...
1
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2answers
177 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
2answers
872 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 $B(0,T)...
1
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0answers
54 views

Prove the following Call and Put relationship: [duplicate]

I need to prove that $$c(S,X,T)=\frac{X}{F}p(S,\frac{F^2}{X},T)$$ where $$F=Se^{(r-q)(T-t)}$$ I am having trouble proving this relationship. Is this relationship even possible? If so, can someone ...
1
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0answers
124 views

Black Scholes Replicating Portfolio Riskfree Asset

Im having a question about this standard derivation of the Black-Scholes formula: http://www.soarcorp.com/research/BS_hedging_portfolio.pdf The paper states $$C=\Delta S+B$$ and finally $\Delta = ...
1
vote
0answers
88 views

Black & Scholes with stochastic interest rate [duplicate]

Consider the following model $$\begin{cases} dS_t=r_tS_tdt+\sigma S_tdW_t, \\ dr_t=adt+\eta dW_t\\ \end{cases} $$ where $W$ is a Brownian motion and $\sigma, a ,b, \eta$ are positive constants. I ...
1
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0answers
80 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 $\delta$ $\delta=\frac{\partial}{\...
1
vote
0answers
143 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 ...
0
votes
2answers
242 views

How to make the arbitrage if intrinsic value is greater than European call value

It always says if the intrinsic value is greater than European call value, there will be a arbitrage opportunity,but how to construct the portfolio $(S_t - K)^+$ or how to make this arbitrage. By the ...
0
votes
3answers
55 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 $\$110$ ...