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Questions tagged [call]

The tag has no usage guidance.

0
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1answer
59 views

Decreasing value of the Put option with increasing Time to maturity [closed]

Can you think of a situation when increasing the time to maturity lowers the value of a put option? If yes, show the example pls.
0
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2answers
110 views

Proof Black Scholes Theta

I saw the following proof of theta in a paper I read, and I thought it looked pretty neat. Unfortunately I don't understand the step that they do. This is what they do: Now, I don't get how they go ...
0
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0answers
45 views

Synthetic Long Call in practice

I have researched Synthetic Long Calls on various texts, including John C.Hull and I also read some papers on Portfolio Insurance by Abken,Israelov and Nielsen, Aliprantis, Bertrand and Prigent, Lee, ...
0
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0answers
145 views

Skew vs Normalised Skew

In this paper, https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true, it states that, SPX Implied Normalized Skew: (25D Put IV - 25D Call IV)/(...
0
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0answers
49 views

If an American call option is valued at $V_t = \max\{ \text{payoff}_t, E V_{t+1}/(1+r)\}$, is it always the latter?

So I am told that we value American call options at time $t$ using $V_t = \max\{ \text{payoff}_t, E V_{t+1}/(1+r)\}$ Will this always be equal to $E V_{t+1} /(1+r)$ if there are no dividends?
2
votes
1answer
85 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 ...
0
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0answers
90 views

Higher Vega with ATM options when Spot is higher

Which would have larger vega, an ATM call option at spot 100 or an ATM call option at spot 200. Apparently the answer is the one with ATM at spot 200. I am not sure how you get this answer. Why ...
0
votes
1answer
357 views

Value of Call Option as Volatility goes to Infinity

Why would the value of a call option go infinity as volatility goes to infinity? I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
0
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0answers
46 views

Different versions of Put-Call Parity

Why is it stated sometimes that $C - P = F$ and in wikipedia it statest that $C - P = D(F-K)$, where D is the discount factor and K is the strike (of both the call and put?). Is this just affected ...
0
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1answer
258 views

Bachelier model call: computation of delta of a call option

The price of a call with a stock with Bachellier process as its underlying and zero interest rate is giving by: $$C(t)=(S(t)-K)\Phi(\frac{S(t)-K}{\sigma \sqrt{T-t}})+\sigma \sqrt{T-t} \phi(\frac{S(t)-...
1
vote
1answer
247 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 ...
0
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0answers
63 views

Arbitrage opportunity with call options? [duplicate]

Call options with strikes 100, 120, and 130 on the same underlying asset and with the same maturity are trading for 8, 5, and 3, respectively (there is no bid-ask spread). Is there an arbitrage ...
0
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1answer
95 views

Asian Call Option

An Asian call option with the average strike payoff, uses the “averaging” to reduce the effect of volatility. Why is this so?
2
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2answers
168 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
348 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 ...
0
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0answers
43 views

call option exercise

I am stuck in this exercise and do not know how to solve it, maybe someone can help me :) We have a special type of European call, the buyer pays the option price at maturity, but only if the option ...
0
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1answer
115 views

option call question

i have a question regarding a call option exercise i cant get my head around The price of a stock is 100, the continuously compounded risk free rate is 5%. The strike price of an european call option ...
0
votes
1answer
134 views

Down-Out Call and Vanilla call price

We all know from text books and practice that a knock out call is usually cheaper than a vanilla call option. Economically speaking, this comes from the fact that there is a probability bigger than ...
1
vote
1answer
231 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
1answer
108 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
0answers
79 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 ...
0
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0answers
232 views

Question about Delta Hedging

So in Delta Hedging, we know that the delta value gives us the hedge ratio between the option and the stock. For example, if we are long 10 shares of stock, and the delta value is 0.5, then we would ...
-3
votes
1answer
269 views

Log-moneyness definition [closed]

Define the time-0 log-moneyness of a call on stock $S$ with strike $K$ and expiry $T$ to be: $$\log(S(0)\exp(rT)/K)$$ What does it mean for the strikes K to be at-the-log-moneyness?? I guessed this ...
0
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0answers
95 views

Difference between writing a call and selling a call

I'm just trying to understand the mechanism behind the two, and why they are used interchangeably. What if someone decides to write a call on a Stock, and I decide to buy the Call (Let's say the ...
0
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1answer
188 views

Black-Scholes European call price taking limits

Given that the Black-Scholes formula for a European Call is given by: $$C(S,t)=Se^{-D(T-t)}N(d_1)-Ke^{-r(T-t)}N(d_2)$$ $S$ is stock price, $K$ is strike price When I take limit as $t\rightarrow T^-$...
-1
votes
2answers
73 views

European call options and strikes [closed]

We consider 2 European call options with the same underlying asset, the same maturity date $T$ and with 2 different strikes $K_1$ and $K_2$ such that $K_1\leq K_2$. We denote $C^1_{0}$ and $C^{2}_{0}$ ...
0
votes
0answers
616 views

Relationship between implied volatility of European and American put

Why is the implied volatility of an American put (on a non-dividend paying stock) lower than that of an European put on the same stock? For example suppose there is a put option that is priced at $1....
-1
votes
1answer
433 views

Put call parity in practice

I understand the Wikipedia article for put-call parity on a theoretical level: if you magically had portfolios consisting of 1) long a call, short a put, and 2) long the stock, short a discounted ...
2
votes
1answer
88 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? ...
4
votes
1answer
95 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 $...
0
votes
2answers
197 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 ...
8
votes
3answers
9k 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.
3
votes
1answer
164 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 ...
3
votes
1answer
173 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,...
0
votes
2answers
154 views

When a stock's price could suddenly drop to zero before expire. does black-scholes misprice the option? Too high or Too low?

Quantitative Question – BLACK SCHOLES Consider a call option on a stock. Assume that Black-Scholes prices the option correctly if all of the assumptions of Black-Scholes hold true. Assume in addition ...
0
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0answers
57 views

how to understand the zero vol condition in Heston stochastic vol model

I can't understand one of the boundary conditions in Heston's model: $$c(t,s,0) = (s-e^{-r(T-t)}K)^+$$ Why the current vol is zero can deduce such result. here $c(t,s,v)$ $s$ is current price and $v$ ...
-2
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2answers
4k views

why is the delta of a short call option negative? [closed]

Why is the delta of a short call option negative? In Black-Scholes-Merton equation the delta of a call option is always a probability function therefore it does not imply such a consequence. How do I ...
5
votes
1answer
270 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. ...
2
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0answers
153 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 ...
2
votes
2answers
312 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}...
3
votes
1answer
97 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)}}{\...
1
vote
1answer
88 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
1answer
1k views

Use of cash delta vs forward delta and the mirror image rule

There has been no mention in this text of why this formula uses forward delta not cash delta. Why should have this been obvious to the reader? How can a put be delta neutral at 30%, what does this ...
0
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3answers
54 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 $\$110$ ...
6
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0answers
581 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 $S2$ = ...
-1
votes
1answer
237 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 !
1
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0answers
78 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}{\...
4
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5answers
695 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 ...
1
vote
2answers
153 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
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2answers
994 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 ...