BA II Plus calculator for FRM Part I quant and valuation

2. Convert rates with eˣ and LN

Continuous compounding runs through the exponential keys. Press 2ND eˣ to exponentiate a continuously compounded rate, and LN to move an effective factor back to a continuous rate.

3. Load the TVM worksheet for discounting

For a single expected cash flow, set P/Y to 1, store the horizon in N, the discount rate in I/Y, PMT at 0, and the exposure in FV. This is the discounting backbone of counterparty and bond problems alike.

4. Solve the present value

With four TVM fields known, press CPT then the unknown key. CPT PV discounts the stored exposure back to today; the sign convention returns it as a negative figure.

5. Bracket a yield to read sensitivity

To gauge interest-rate risk, re-price a bond at a slightly higher and lower yield, then combine the two prices. This gives an effective duration without a closed-form derivative.

Continuously compounded rate to an effective annual rate

A funding desk quotes a 8% continuously compounded rate. Convert it to the equivalent effective annual rate with the exponential key: key .08, press 2ND eˣ, then subtract 1.

eˣ turns the continuously compounded rate into a growth factor; subtracting 1 leaves the effective annual rate. This is the reverse of the LN step you use to move an effective rate back to a continuous one.

Discount an expected counterparty exposure to present value

A single expected exposure of $10,000,000 falls due in 3 years. At a 4% risk-free discount rate, discount it to today using the TVM worksheet with annual compounding.

CPT PV returns a negative number because the future exposure and its present value sit on opposite sides of the cash-flow sign convention. The discounted exposure is about $8.89m.

Price an annual-coupon bond from its yield

A 4-year bond pays a 5% annual coupon on 100 face value and yields 6%. Store the cash flows in the TVM worksheet and solve for present value.

CPT PV shows -96.5349; the clean price is 96.5349 per 100 face. It trades below par because the 5% coupon is under the 6% yield — a discount bond.

Effective duration by re-pricing the bond

Take the same 4-year 5% bond priced at 96.5349 (yield 6%). Re-price it at 5.5% and 6.5%, then apply effective duration = (P− − P+) / (2 · P0 · Δy) with Δy = 0.005.

Effective duration is about 3.51, so a 100bp parallel yield move changes the price by roughly 3.51%. Re-pricing at bracketing yields is the model-free way to get duration when a closed form is awkward.

Present value of an expected credit loss (PD × LGD × EAD)

A one-name limit carries a 3% one-year default probability, 60% loss-given-default, and $10,000,000 exposure-at-default. Build the expected loss as a product chain — .03 × .60 × 10000000 — then discount that loss two years out at a 5% risk-free rate on the TVM worksheet.

The expected loss itself is $180,000 (0.03 × 0.60 × 10,000,000); discounting two years at 5% brings its present value to about $163,265. Decomposing risk into PD, LGD, and EAD before discounting is the credit-risk analogue of pricing any other future cash flow.