NVIDIA Corp (NVDA) is currently priced S = $450. Price 66 DTE calls and puts for strikes from $420 to $480, incremented by $10. Currently have = 43% and r = 5.3% (r = 0.053).

Note: You will need to set your working directory to where the OptionAnayltics file is located. Also note default BS function pricing is for call prices, set typ = p to price puts.

source('OptionAnalytics.r')

s0 <- 450

## Create a sequence of strike prices

k <- seq(420,480,by=10)

sig <- 0.43

r <- 0.053

t66 <- 66/365

## Price all the call prices, then the put prices

c1 <- round(BS(s0,k,sig,r,t66),2)

p1 <- round(BS(s0,k,sig,r,t66,typ='p'),2)

## create a data.frame of strikes with call and put prices opt1 <- data.frame(strike=k,calls=c1,puts=p1)

opt1

## strike calls puts

##1 420 51.40 17.40

##2 430 45.38 21.28

##3 440 39.85 25.66

##4 450 34.81 30.52

##5 460 30.25 35.87

##6 470 26.16 41.67

##7 480 22.50 47.92

Example: A long butterfly spread is a neutral position and is made when traders believe the price will remain in a tight range. It consists of long K1 and K3 strike calls/puts and short 2 K2 calls/puts where K1 < K2 < K3 and K1,K3 are equidistant from K2. The position is created using only calls or puts.

Using the information above create K = 430/450/470 long call butterfly position. Compute the following information for position with 27, 15 and 0 DTE, across price range given below:

(a) Profit/Loss (P/L) for 27, 15 and 0 DTE. Note: you cannot use the BS() function when t = 0. (b) Delta for 27 and 15 DTE (cant compute Delta with DTE = 0)

(c) P/Lfor27DTEassuming=23%and=63%

# cost0 determines the cost of the trade. If it's positive, it's a debit and if it's negative