Suppose you work for a financial institution, and your team is tasked with pricing European call options on a stock. The stock in question is currently trading at $100 per share, and the risk-free interest rate is 5% per annum. The volatility of the stock is estimated to be 20% per annum. The option has a maturity of 6 months.
pv <- 100
r <- 0.05 #Annual Risk-Free Interest Rate
t <- 0.5 #Time
FV <- pv * (1 + r)^t
FV## [1] 102.4695Bsed on the calculations, it is predicted the stock price will rise up to $102.47 in 6 months. Furthermore, using Black-Scholes Formula we can calculate the Fair Price 6 months later.
pv <- 100
x <- 100
r <- 0.05
t <- 0.5
sig <- 0.2
d1 <- (log(pv / x) + (r + (sig^2 / 2)) * t) / (sig * sqrt(t))
d2 <- d1 - sig * sqrt(t)
Blk <- pv * pnorm(d1) - x * exp(-r * t) * pnorm(d2)
Blk## [1] 6.888729The fair price for the next 6 months is $6.89
Let’s consider a scenario where an investor is evaluating two investment opportunities: investing in a stock market index fund or depositing the same amount of money in a savings account. The investor has $12,000 to invest and has to decide whether to invest it now or wait for a year. Suppose the expected return from the stock market index fund is 9% per year, while the interest rate on the savings account is 2% per year.
pv <- 12000
r_stock <- 0.09
r_saving <- 0.02
n <- 1 #for years
fv_stock <- pv * (1 + r_stock)^n
fv_savings <- pv * (1 + r_saving)^n
cat("Nilai hasil investasi saham", fv_stock, "\n")## Nilai hasil investasi saham 13080cat("Nilai hasil investasi depostito", fv_savings, "\n")## Nilai hasil investasi depostito 12240We can see how much money is earned after investing in stocks or deposits with an interest assumption of 9% and done for 1 year or 12 months.
Calculate the future value of an investment with regular contributions. The investment is compounded monthly, and the interest rate varies over time. Assumptions: * Initial investment (PV): $10,000 * Monthly contribution: $500 * Time horizon: 6 years * Annual interest rate: - First year: 6% - Second year: 7% - Third year: 8% - Fourth year: 9% - Fifth year: 9.5%
PV <- 10000
monthly_contribution <- 500
years <- 6
months <- years * 12
interest_rates <- c(0.06, 0.07, 0.08, 0.09, 0.095, 0.06)
FV <- numeric(months + 1)
FV[1] <- PV
for (i in 1:months) {
year <- ceiling(i / 12)
monthly_rate <- interest_rates[year]
FV[i + 1] <- FV[i] * (1 + monthly_rate/12) + monthly_contribution
}
tail(FV, 1)## [1] 61515.33Based on these results, it can be concluded that when having $10000 by adding monthly of 500 and investing for 6 years with floating interest rates ranging from 6%, 7%, 8%, 9% 9.5% , 6% (Assumption) since on the question was only 5 years. Will brings us to the total balance of $61515.33 By The End of the 5 years Period.