Interest-rate optionality · Black-76

Floating-rate loan with cap & floor — Black-76 valuation

Lender's position = straight floating loan + long floor (K₁) − short cap (K₂). Each caplet/floorlet is European, so it is valued in closed form with Black-76. Live inputs; values reconcile to the underlying workbook.

Notional 10,00,000

Maturity 2 yrs

Coupon freq Quarterly (τ=0.25)

Cap K₂ 4.20%

Floor K₁ 3.80%

Black vol σ 0.50%

Par swap rate 4.1013%

Spread 0.00%

Day count Act, dt=0.25

Controls

Cap K₂: 4.20% Floor K₁: 3.80% Black vol σ: 0.50%

Valuation to the bank / lender

Cap value (short)

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Floor value (long)

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Straight floating loan

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Loan with cap/floor

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Caplet / floorlet detail

i	t₁	t₂	v=σ√t₁	F(t₁,t₂)	Caplet V	Floorlet V

Value by reset period (₹)

Validation checks

Check	Value	Result

Read the optionality methodology →

Reproduces the workbook's Black-76 valuation of a capped/floored floating loan. Illustrative loan; method and figures are the author's own working, not client data or code.